# Сюрпризы таблицы умножения

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```&Ecirc;&Agrave;&Euml;&Aring;&Eacute;&Auml;&Icirc;&Ntilde;&Ecirc;&Icirc;&Iuml;
&laquo;&Ecirc;&Acirc;&Agrave;&Iacute;&Ograve;&Agrave;&raquo;
&Ntilde;&thorn;&eth;&iuml;&eth;&egrave;&ccedil;&ucirc; &ograve;&agrave;&aacute;&euml;&egrave;&ouml;&ucirc;
&oacute;&igrave;&iacute;&icirc;&aelig;&aring;&iacute;&egrave;&yuml;
&Acirc;&iuml;&aring;&eth;&acirc;&ucirc;&aring; &ograve;&agrave;&aacute;&euml;&egrave;&ouml;&agrave; &Iuml;&egrave;&ocirc;&agrave;&atilde;&icirc;&eth;&agrave; &iuml;&eth;&egrave;&igrave;&aring;&eth;&iacute;&icirc; &acirc; &ograve;&agrave;&ecirc;&icirc;&igrave; &acirc;&egrave;&auml;&aring;, &acirc; &ecirc;&agrave;&ecirc;&icirc;&igrave; &igrave;&ucirc; &aring;&aring;
&iacute;&agrave;&otilde;&icirc;&auml;&egrave;&igrave; &iacute;&agrave; &icirc;&aacute;&euml;&icirc;&aelig;&ecirc;&agrave;&otilde; &ograve;&aring;&ograve;&eth;&agrave;&auml;&aring;&eacute;,
&iuml;&icirc;&yuml;&acirc;&egrave;&euml;&agrave;&ntilde;&uuml; &acirc; &ntilde;&icirc;&divide;&egrave;&iacute;&aring;&iacute;&egrave;&egrave; &iacute;&aring;&icirc;&iuml;&egrave;&ocirc;&agrave;&atilde;&icirc;&eth;&aring;&eacute;&ouml;&agrave; &Iacute;&egrave;&ecirc;&icirc;&igrave;&agrave;&otilde;&agrave; &Atilde;&aring;&eth;&agrave;&ccedil;&ntilde;&ecirc;&icirc;&atilde;&icirc;
(III &acirc;&acirc;.). &Acirc; &aring;&atilde;&icirc; &laquo;&Acirc;&acirc;&aring;&auml;&aring;&iacute;&egrave;&egrave; &acirc;
&agrave;&eth;&egrave;&ocirc;&igrave;&aring;&ograve;&egrave;&ecirc;&oacute;&raquo; &ograve;&agrave;&aacute;&euml;&egrave;&ouml;&agrave; &acirc;&ucirc;&iuml;&icirc;&euml;&iacute;&aring;&iacute;&agrave;
&acirc; &egrave;&icirc;&iacute;&egrave;&eacute;&ntilde;&ecirc;&icirc;&eacute; &iacute;&oacute;&igrave;&aring;&eth;&agrave;&ouml;&egrave;&egrave;. &Iuml;&icirc; &ntilde;&euml;&icirc;&acirc;&agrave;&igrave; &Iacute;&egrave;&ecirc;&icirc;&igrave;&agrave;&otilde;&agrave;, &yacute;&ograve;&agrave; &ograve;&agrave;&aacute;&euml;&egrave;&ouml;&agrave; &acirc;&icirc;&ntilde;&otilde;&icirc;&auml;&egrave;&ograve; &laquo;&ecirc; &ntilde;&agrave;&igrave;&icirc;&igrave;&oacute; &Iuml;&egrave;&ocirc;&agrave;&atilde;&icirc;&eth;&oacute;&raquo;.
1 2
3
4
2 4
6
8 10 12 14 16 18
3 6
9
12 15 18 21 24 27
4 8
12 16 20 24 28 32 36
5
6
7
8
9
5 10 15 20 25 30 35 40 45
6 12 18 24 30 36 42 48 54
7 14 21 28 35 42 49 56 63
8 16 24 32 40 48 56 64 72
9 18 27 36 45 54 63 72 81
&ETH;&egrave;&ntilde;.1. &Ograve;&agrave;&aacute;&euml;&egrave;&ouml;&agrave; &Iuml;&egrave;&ocirc;&agrave;&atilde;&icirc;&eth;&agrave;
&Aacute;&icirc;&euml;&aring;&aring; &auml;&eth;&aring;&acirc;&iacute;&egrave;&aring; &ograve;&agrave;&aacute;&euml;&egrave;&ouml;&ucirc; &oacute;&igrave;&iacute;&icirc;&aelig;&aring;&iacute;&egrave;&yuml; &icirc;&aacute;&iacute;&agrave;&eth;&oacute;&aelig;&aring;&iacute;&ucirc; &acirc; &igrave;&aring;&ntilde;&icirc;&iuml;&icirc;&ograve;&agrave;&igrave;&ntilde;&ecirc;&egrave;&otilde;
&atilde;&euml;&egrave;&iacute;&yuml;&iacute;&ucirc;&otilde; &ograve;&agrave;&aacute;&euml;&egrave;&divide;&ecirc;&agrave;&otilde;  &egrave;&otilde; &laquo;&acirc;&icirc;&ccedil;&eth;&agrave;&ntilde;&ograve;&raquo; &icirc;&ecirc;&icirc;&euml;&icirc; 5 &ograve;&ucirc;&ntilde;&yuml;&divide; &euml;&aring;&ograve;.
&Ograve;&agrave;&aacute;&euml;&egrave;&ouml;&agrave; &oacute;&igrave;&iacute;&icirc;&aelig;&aring;&iacute;&egrave;&yuml; &ntilde;&ecirc;&eth;&ucirc;&acirc;&agrave;&aring;&ograve; &acirc;
&ntilde;&aring;&aacute;&aring; &igrave;&iacute;&icirc;&aelig;&aring;&ntilde;&ograve;&acirc;&icirc; &ccedil;&agrave;&igrave;&aring;&divide;&agrave;&ograve;&aring;&euml;&uuml;&iacute;&ucirc;&otilde; &igrave;&agrave;&ograve;&aring;&igrave;&agrave;&ograve;&egrave;&divide;&aring;&ntilde;&ecirc;&egrave;&otilde; &ccedil;&agrave;&ecirc;&icirc;&iacute;&icirc;&igrave;&aring;&eth;&iacute;&icirc;&ntilde;&ograve;&aring;&eacute;,
&iuml;&icirc;&egrave;&ntilde;&ecirc; &ecirc;&icirc;&ograve;&icirc;&eth;&ucirc;&otilde; &igrave;&icirc;&aelig;&aring;&ograve; &iuml;&eth;&aring;&acirc;&eth;&agrave;&ograve;&egrave;&ograve;&uuml;&ntilde;&yuml; &acirc; &oacute;&acirc;&euml;&aring;&ecirc;&agrave;&ograve;&aring;&euml;&uuml;&iacute;&icirc;&aring; &ccedil;&agrave;&iacute;&yuml;&ograve;&egrave;&aring;, &ntilde;&oacute;&euml;&yuml;&ugrave;&aring;&aring; &iacute;&aring;&igrave;&agrave;&euml;&icirc; &ntilde;&thorn;&eth;&iuml;&eth;&egrave;&ccedil;&icirc;&acirc;.
&Iacute;&agrave;&ccedil;&icirc;&acirc;&aring;&igrave; &ecirc;&acirc;&agrave;&eth;&ograve;&aring;&ograve;&icirc;&igrave; &divide;&aring;&ograve;&ucirc;&eth;&aring; &divide;&egrave;&ntilde;&euml;&agrave; &ograve;&agrave;&aacute;&euml;&egrave;&ouml;&ucirc; &Iuml;&egrave;&ocirc;&agrave;&atilde;&icirc;&eth;&agrave;, &eth;&agrave;&ntilde;&iuml;&icirc;&euml;&icirc;&aelig;&aring;&iacute;&iacute;&ucirc;&otilde; &acirc; &acirc;&aring;&eth;&oslash;&egrave;&iacute;&agrave;&otilde; &iacute;&aring;&ecirc;&icirc;&ograve;&icirc;&eth;&icirc;&atilde;&icirc;
&ecirc;&acirc;&agrave;&auml;&eth;&agrave;&ograve;&agrave;. &Icirc;&ecirc;&agrave;&ccedil;&ucirc;&acirc;&agrave;&aring;&ograve;&ntilde;&yuml;, &divide;&ograve;&icirc; &aring;&ntilde;&euml;&egrave;
&ntilde;&ograve;&icirc;&eth;&icirc;&iacute;&ucirc; &yacute;&ograve;&icirc;&atilde;&icirc; &ecirc;&acirc;&agrave;&auml;&eth;&agrave;&ograve;&agrave; &iuml;&agrave;&eth;&agrave;&euml;&euml;&aring;&euml;&uuml;&iacute;&ucirc; &auml;&egrave;&agrave;&atilde;&icirc;&iacute;&agrave;&euml;&yuml;&igrave; &ograve;&agrave;&aacute;&euml;&egrave;&ouml;&ucirc; &Iuml;&egrave;&ocirc;&agrave;&atilde;&icirc;&eth;&agrave;, &ograve;&icirc; &ntilde;&oacute;&igrave;&igrave;&ucirc; &auml;&egrave;&agrave;&atilde;&icirc;&iacute;&agrave;&euml;&uuml;&iacute;&ucirc;&otilde; &divide;&egrave;&ntilde;&aring;&euml;
&ecirc;&acirc;&agrave;&eth;&ograve;&aring;&ograve;&agrave; &eth;&agrave;&acirc;&iacute;&ucirc; (&eth;&egrave;&ntilde;.2). &Aring;&ntilde;&euml;&egrave; &ntilde;&ograve;&icirc;&eth;&icirc;&iacute;&ucirc; &ecirc;&acirc;&agrave;&auml;&eth;&agrave;&ograve;&agrave; &iuml;&agrave;&eth;&agrave;&euml;&euml;&aring;&euml;&uuml;&iacute;&ucirc; &ntilde;&ograve;&icirc;&eth;&icirc;&iacute;&agrave;&igrave; &ograve;&agrave;&aacute;&euml;&egrave;&ouml;&ucirc;, &ograve;&icirc; &eth;&agrave;&acirc;&iacute;&ucirc; &iuml;&eth;&icirc;&egrave;&ccedil;&acirc;&aring;&auml;&aring;&iacute;&egrave;&yuml; &auml;&egrave;&agrave;&atilde;&icirc;&iacute;&agrave;&euml;&uuml;&iacute;&ucirc;&otilde; &divide;&egrave;&ntilde;&aring;&euml; &ecirc;&acirc;&agrave;&eth;&ograve;&aring;&ograve;&agrave;. &Aring;&ntilde;&euml;&egrave; &iuml;&eth;&egrave; &yacute;&ograve;&icirc;&igrave; &ecirc;&acirc;&agrave;&auml;&eth;&agrave;&ograve; &eth;&agrave;&ntilde;&iuml;&icirc;&euml;&icirc;&aelig;&aring;&iacute; &ntilde;&egrave;&igrave;&igrave;&aring;&ograve;&eth;&egrave;&divide;&iacute;&icirc; &atilde;&euml;&agrave;&acirc;&iacute;&icirc;&eacute; &auml;&egrave;&agrave;&atilde;&icirc;&iacute;&agrave;&euml;&egrave; &ograve;&agrave;&aacute;&euml;&egrave;&ouml;&ucirc; &Iuml;&egrave;&ocirc;&agrave;&atilde;&icirc;&eth;&agrave;, &ograve;&icirc; &ntilde;&oacute;&igrave;&igrave;&agrave;
&acirc;&ntilde;&aring;&otilde; &divide;&egrave;&ntilde;&aring;&euml; &ecirc;&acirc;&agrave;&eth;&ograve;&aring;&ograve;&agrave;  &ecirc;&acirc;&agrave;&auml;&eth;&agrave;&ograve; &iacute;&aring;&ecirc;&icirc;&ograve;&icirc;&eth;&icirc;&atilde;&icirc; &iacute;&agrave;&ograve;&oacute;&eth;&agrave;&euml;&uuml;&iacute;&icirc;&atilde;&icirc; &divide;&egrave;&ntilde;&euml;&agrave;, &egrave;
&yacute;&ograve;&icirc; &ntilde;&acirc;&icirc;&eacute;&ntilde;&ograve;&acirc;&icirc; &yuml;&acirc;&euml;&yuml;&aring;&ograve;&ntilde;&yuml; &otilde;&icirc;&eth;&icirc;&oslash;&aring;&eacute; &egrave;&euml;2
&euml;&thorn;&ntilde;&ograve;&eth;&agrave;&ouml;&egrave;&aring;&eacute; &ograve;&icirc;&aelig;&auml;&aring;&ntilde;&ograve;&acirc;&agrave;: a + b =
&gt;
C
8 16 24 32 40 48 56 64 72
&egrave;&igrave;&aring;&iacute;&iacute;&icirc;: &ecirc;&agrave;&aelig;&auml;&icirc;&aring; &divide;&egrave;&ntilde;&euml;&icirc; &ograve;&agrave;&aacute;&euml;&egrave;&ouml;&ucirc;
&eth;&agrave;&acirc;&iacute;&icirc; &iuml;&eth;&icirc;&egrave;&ccedil;&acirc;&aring;&auml;&aring;&iacute;&egrave;&thorn; &iacute;&icirc;&igrave;&aring;&eth;&agrave; &ntilde;&ograve;&eth;&icirc;&ecirc;&egrave; &egrave; &iacute;&icirc;&igrave;&aring;&eth;&agrave; &ntilde;&ograve;&icirc;&euml;&aacute;&ouml;&agrave;, &iacute;&agrave; &iuml;&aring;&eth;&aring;&ntilde;&aring;&divide;&aring;&iacute;&egrave;&egrave; &ecirc;&icirc;&ograve;&icirc;&eth;&ucirc;&otilde; &icirc;&iacute;&icirc; &ntilde;&ograve;&icirc;&egrave;&ograve;.
&Aring;&ntilde;&euml;&egrave; &ouml;&aring;&iacute;&ograve;&eth;&icirc;&igrave; &ecirc;&acirc;&agrave;&eth;&ograve;&aring;&ograve;&agrave; &ograve;&icirc;&aelig;&aring; &yuml;&acirc;&euml;&yuml;&aring;&ograve;&ntilde;&yuml; &divide;&egrave;&ntilde;&euml;&icirc; &ograve;&agrave;&aacute;&euml;&egrave;&ouml;&ucirc; &Iuml;&egrave;&ocirc;&agrave;&atilde;&icirc;&eth;&agrave;,
&ograve;&icirc; &icirc;&iacute;&icirc; &eth;&agrave;&acirc;&iacute;&icirc; &ntilde;&eth;&aring;&auml;&iacute;&aring;&igrave;&oacute; &agrave;&eth;&egrave;&ocirc;&igrave;&aring;&ograve;&egrave;&divide;&aring;&ntilde;&ecirc;&icirc;&igrave;&oacute; &divide;&egrave;&ntilde;&aring;&euml; &yacute;&ograve;&icirc;&atilde;&icirc; &ecirc;&acirc;&agrave;&eth;&ograve;&aring;&ograve;&agrave;
(&eth;&egrave;&ntilde;.3). &Egrave; &icirc;&iuml;&egrave;&eth;&agrave;&yuml;&ntilde;&uuml; &iacute;&agrave; &yacute;&ograve;&icirc; &ntilde;&acirc;&icirc;&eacute;&ntilde;&ograve;&acirc;&icirc;, &euml;&aring;&atilde;&ecirc;&icirc; &auml;&icirc;&ecirc;&agrave;&ccedil;&agrave;&ograve;&uuml;, &divide;&ograve;&icirc; &ntilde;&oacute;&igrave;&igrave;&agrave;
&acirc;&ntilde;&aring;&otilde; &divide;&egrave;&ntilde;&aring;&euml; &ograve;&agrave;&aacute;&euml;&egrave;&ouml;&ucirc; &Iuml;&egrave;&ocirc;&agrave;&atilde;&icirc;&eth;&agrave;, &eth;&agrave;&ntilde;&iuml;&icirc;&euml;&icirc;&aelig;&aring;&iacute;&iacute;&ucirc;&otilde; &acirc;&iacute;&oacute;&ograve;&eth;&egrave; &ouml;&aring;&iacute;&ograve;&eth;&agrave;&euml;&uuml;&iacute;&icirc;&ntilde;&egrave;&igrave;&igrave;&aring;&ograve;&eth;&egrave;&divide;&iacute;&icirc;&eacute; &ocirc;&egrave;&atilde;&oacute;&eth;&ucirc; &iuml;&icirc;&ecirc;&agrave;&ccedil;&agrave;&iacute;&iacute;&icirc;&atilde;&icirc; &iacute;&agrave; &eth;&egrave;&ntilde;&oacute;&iacute;&ecirc;&aring; 4 &acirc;&egrave;&auml;&agrave;, &eth;&agrave;&acirc;&iacute;&agrave; &iuml;&eth;&icirc;&egrave;&ccedil;&acirc;&aring;&auml;&aring;&iacute;&egrave;&thorn; &ouml;&aring;&iacute;&ograve;&eth;&agrave;&euml;&uuml;&iacute;&icirc;&atilde;&icirc; &divide;&egrave;&ntilde;&euml;&agrave; &iacute;&agrave;
&ecirc;&icirc;&euml;&egrave;&divide;&aring;&ntilde;&ograve;&acirc;&icirc; &divide;&egrave;&ntilde;&aring;&euml; &ocirc;&egrave;&atilde;&oacute;&eth;&ucirc;. &Iuml;&eth;&egrave;
&icirc;&ograve;&ntilde;&oacute;&ograve;&ntilde;&ograve;&acirc;&egrave;&egrave; &ouml;&aring;&iacute;&ograve;&eth;&agrave;&euml;&uuml;&iacute;&icirc;&atilde;&icirc; &divide;&egrave;&ntilde;&euml;&agrave;
&acirc;&igrave;&aring;&ntilde;&ograve;&icirc; &iacute;&aring;&atilde;&icirc; &aacute;&aring;&eth;&aring;&ograve;&ntilde;&yuml; &auml;&eth;&icirc;&aacute;&iacute;&icirc;&aring; &divide;&egrave;&ntilde;&euml;&icirc;,
&eth;&agrave;&acirc;&iacute;&icirc;&aring; &iuml;&eth;&icirc;&egrave;&ccedil;&acirc;&aring;&auml;&aring;&iacute;&egrave;&thorn; &atilde;&egrave;&iuml;&icirc;&ograve;&aring;&ograve;&egrave;&divide;&aring;&ntilde;&ecirc;&egrave;&otilde; &auml;&eth;&icirc;&aacute;&iacute;&ucirc;&otilde; &iacute;&icirc;&igrave;&aring;&eth;&agrave; &ntilde;&ograve;&eth;&icirc;&ecirc;&egrave; &egrave; &iacute;&icirc;&igrave;&aring;&eth;&agrave; &ntilde;&ograve;&icirc;&euml;&aacute;&ouml;&agrave;.
&Ntilde;&ecirc;&oacute;&divide;&iacute;&oacute;&thorn;, &iacute;&agrave; &iuml;&aring;&eth;&acirc;&ucirc;&eacute; &acirc;&ccedil;&atilde;&euml;&yuml;&auml;, &ccedil;&agrave;&auml;&agrave;&divide;&oacute; &acirc;&ucirc;&divide;&egrave;&ntilde;&euml;&aring;&iacute;&egrave;&yuml; &ntilde;&oacute;&igrave;&igrave;&ucirc; &acirc;&ntilde;&aring;&otilde; &divide;&egrave;&ntilde;&aring;&euml; &ograve;&agrave;&aacute;&euml;&egrave;&ouml;&ucirc; &Iuml;&egrave;&ocirc;&agrave;&atilde;&icirc;&eth;&agrave; &igrave;&icirc;&aelig;&iacute;&icirc; &eth;&aring;&oslash;&egrave;&ograve;&uuml;, &iuml;&icirc;&euml;&oacute;&divide;&egrave;&acirc; &iuml;&eth;&egrave; &yacute;&ograve;&icirc;&igrave; &iacute;&aring;&igrave;&agrave;&euml;&icirc;&aring;
&oacute;&auml;&icirc;&acirc;&icirc;&euml;&uuml;&ntilde;&ograve;&acirc;&egrave;&aring;: &iuml;&icirc;&ntilde;&ecirc;&icirc;&euml;&uuml;&ecirc;&oacute; 1 + 2 +
+ 3 +  + 9 = 45, &ograve;&icirc; &ntilde;&oacute;&igrave;&igrave;&agrave; &divide;&egrave;&ntilde;&aring;&euml;
&ograve;&agrave;&aacute;&euml;&egrave;&ouml;&ucirc; &aacute;&oacute;&auml;&aring;&ograve; &eth;&agrave;&acirc;&iacute;&agrave;
9 18 27 36 45 54 63 72 81
1 ⋅ 45 + 2 ⋅ 45 + 3 ⋅ 45 +...+9 ⋅ 45 =
1 2
3
4
5
6
7
8
9
2 4
6
8
10 12 14 16 18
3 6
9
12 15 18 21 24 27
4 8
12 16 20 24 28 32 36
5 10 15 20 25 30 35 40 45
6 12 18 24 30 36 42 48 54
7 14 21 28 35 42 49 56 63
8 16 24 32 40 48 56 64 72
9 18 27 36 45 54 63 72 81
6 + 18 = 4 + 20, 6 30 = 12 15,
7 + 2 7 9 + 9 = 256
&ETH;&egrave;&ntilde;.2
6
7
8
9
1 2
3
4
5
2 4
6
8
10 12 14 16 18
3 6
9
12 15 18 21 24 27
4 8
12 16 20 24 28 32 36
5 10 15 20 25 30 35 40 45
6 12 18 24 30 36 42 48 54
7 14 21 28 35 42 49 56 63
&ETH;&egrave;&ntilde;.3
6
7
8
9
3
4
5
2 4
6
8
10 12 14 16 18
3 6
9
12 15 18 21 24 27
4 8
12 16 20 24 28 32 36
5 10 15 20 25 30 35 40 45
6 12 18 24 30 36 42 48 54
7 14 21 28 35 42 49 56 63
8 16 24 32 40 48 56 64 72
9 18 27 36 45 54 63 72 81
S=12 13=156, S =7,5 6,5 12=585
&ETH;&egrave;&ntilde;.4
2
2
C
= 45 ⋅ 45 = 2025 .
2
1
&gt;
= 45 ⋅ 1 + 2 + 3 +...+9 =
20=(9+12+24+35):4
= a + 2ab + b . &Auml;&icirc;&ecirc;&agrave;&ccedil;&agrave;&ograve;&aring;&euml;&uuml;&ntilde;&ograve;&acirc;&agrave;
&yacute;&ograve;&egrave;&otilde; &ntilde;&acirc;&icirc;&eacute;&ntilde;&ograve;&acirc; &iuml;&eth;&icirc;&ntilde;&ograve;&ucirc; &egrave; &icirc;&ntilde;&iacute;&icirc;&acirc;&agrave;&iacute;&ucirc; &iacute;&agrave;
&icirc;&iuml;&eth;&aring;&auml;&aring;&euml;&aring;&iacute;&egrave;&egrave; &ograve;&agrave;&aacute;&euml;&egrave;&ouml;&ucirc; &Iuml;&egrave;&ocirc;&agrave;&atilde;&icirc;&eth;&agrave;, &agrave;
&Ecirc;&eth;&agrave;&ntilde;&egrave;&acirc;&icirc;, &iacute;&aring; &iuml;&eth;&agrave;&acirc;&auml;&agrave; &euml;&egrave;?
&Ccedil;&agrave;&igrave;&aring;&ograve;&egrave;&igrave; &ograve;&agrave;&ecirc;&aelig;&aring;, &divide;&ograve;&icirc; &acirc;&ntilde;&aring; &divide;&egrave;&ntilde;&euml;&agrave;
&ograve;&agrave;&aacute;&euml;&egrave;&ouml;&ucirc; &Iuml;&egrave;&ocirc;&agrave;&atilde;&icirc;&eth;&agrave; &igrave;&icirc;&aelig;&iacute;&icirc; &eth;&agrave;&ccedil;&aacute;&egrave;&ograve;&uuml;
&iacute;&agrave; &auml;&aring;&acirc;&yuml;&ograve;&uuml; &atilde;&eth;&oacute;&iuml;&iuml; &iuml;&icirc; &auml;&aring;&acirc;&yuml;&ograve;&uuml; &divide;&egrave;&ntilde;&aring;&euml; &acirc;
&ecirc;&agrave;&aelig;&auml;&icirc;&eacute; &ograve;&agrave;&ecirc;, &divide;&ograve;&icirc; &iuml;&eth;&icirc;&egrave;&ccedil;&acirc;&aring;&auml;&aring;&iacute;&egrave;&yuml; &divide;&egrave;&ntilde;&aring;&euml; &acirc; &ecirc;&agrave;&aelig;&auml;&icirc;&eacute; &atilde;&eth;&oacute;&iuml;&iuml;&aring; &icirc;&ecirc;&agrave;&aelig;&oacute;&ograve;&ntilde;&yuml;
&eth;&agrave;&acirc;&iacute;&ucirc;&igrave;&egrave; (&eth;&egrave;&ntilde;.5). &ETH;&agrave;&ccedil;&aacute;&egrave;&acirc;&agrave;&yuml; &divide;&egrave;&ntilde;&euml;&agrave;
&iacute;&agrave; &atilde;&eth;&oacute;&iuml;&iuml;&ucirc;, &iacute;&oacute;&aelig;&iacute;&icirc; &ntilde;&icirc;&aacute;&euml;&thorn;&auml;&agrave;&ograve;&uuml; &iuml;&eth;&agrave;&acirc;&egrave;&euml;&icirc;: &divide;&egrave;&ntilde;&euml;&agrave; &icirc;&auml;&iacute;&icirc;&eacute; &atilde;&eth;&oacute;&iuml;&iuml;&ucirc; &auml;&icirc;&euml;&aelig;&iacute;&ucirc;
&ntilde;&ograve;&icirc;&yuml;&ograve;&uuml; &acirc; &ecirc;&euml;&aring;&ograve;&ecirc;&agrave;&otilde; &ograve;&agrave;&aacute;&euml;&egrave;&ouml;&ucirc; &ograve;&agrave;&ecirc;, &divide;&ograve;&icirc;&aacute;&ucirc; &oacute;&ntilde;&ograve;&agrave;&iacute;&icirc;&acirc;&euml;&aring;&iacute;&iacute;&ucirc;&aring; &iacute;&agrave; &iacute;&egrave;&otilde; &oslash;&agrave;&otilde;&igrave;&agrave;&ograve;&iacute;&ucirc;&aring; &euml;&agrave;&auml;&uuml;&egrave; &aacute;&ucirc;&euml;&egrave; &auml;&eth;&oacute;&aelig;&aring;&euml;&thorn;&aacute;&iacute;&ucirc;&igrave;&egrave;,
&ograve;.&aring;. &iacute;&aring; &oacute;&atilde;&eth;&icirc;&aelig;&agrave;&euml;&egrave; &auml;&eth;&oacute;&atilde; &auml;&eth;&oacute;&atilde;&oacute;. &Acirc;
&yacute;&ograve;&icirc;&igrave; &ntilde;&euml;&oacute;&divide;&agrave;&aring; &acirc;&ntilde;&aring; &auml;&aring;&acirc;&yuml;&ograve;&uuml; &iuml;&eth;&icirc;&egrave;&ccedil;&acirc;&aring;&auml;&aring;&iacute;&egrave;&eacute; &aacute;&oacute;&auml;&oacute;&ograve; &eth;&agrave;&acirc;&iacute;&ucirc;
&gt;1 ⋅ 2 ⋅ 3 ⋅ 4 ⋅ 5 ⋅ 6 ⋅ 7 ⋅ 8 ⋅ 9C = &gt;9!C .
2
2
&Iacute;&agrave; &eth;&egrave;&ntilde;&oacute;&iacute;&ecirc;&aring; 6 &acirc; &ograve;&agrave;&aacute;&euml;&egrave;&ouml;&aring; &Iuml;&egrave;&ocirc;&agrave;&atilde;&icirc;&eth;&agrave; &acirc;&ucirc;&auml;&aring;&euml;&aring;&iacute;&ucirc; &laquo;&oacute;&atilde;&icirc;&euml;&ecirc;&egrave;&raquo;. &Ntilde;&oacute;&igrave;&igrave;&ucirc;
&divide;&egrave;&ntilde;&aring;&euml; &acirc; &oacute;&atilde;&icirc;&euml;&ecirc;&agrave;&otilde; &icirc;&aacute;&eth;&agrave;&ccedil;&oacute;&thorn;&ograve; &iuml;&icirc;&ntilde;&euml;&aring;&auml;&icirc;-
1 2
3
4
5
6
7
8
9
&igrave;&oacute;&euml;&aring;
10 12 14 16 18
2 4
6
8
3 6
9
12 15 18 21 24 27
4 8
12 16 20 24 28 32 36
&ETH;&egrave;&ntilde;.8
7 14 21 28 35 42 49 56 63
8 16 24 32 40 48 56 64 72
&gt;
6
7
8
9
3
4
5
2 4
6
8
10 12 14 16 18
3 6
9
12 15 18 21 24 27
4 8
12 16 20 24 28 32 36
5 10 15 20 25 30 35 40 45
6 12 18 24 30 36 42 48 54
7 14 21 28 35 42 49 56 63
8 16 24 32 40 48 56 64 72
&ETH;&egrave;&ntilde;.9
6, 10, 15, ,
&gt;
&gt;
2
C
(&agrave;&iacute;&agrave;&euml;&icirc;&atilde; &ograve;&eth;&aring;-
C
C
&Oacute;&igrave;&iacute;&icirc;&aelig;&aring;&iacute;&egrave;&aring; &acirc; &oslash;&oacute;&ograve;&ecirc;&oacute; &egrave; &acirc;&ntilde;&aring;&eth;&uuml;&aring;&ccedil;
C , ). &Acirc;&icirc; &acirc;&ntilde;&aring;&otilde;
n n +1
1. &Ntilde;&ecirc;&icirc;&euml;&uuml;&ecirc;&icirc; &aacute;&oacute;&auml;&aring;&ograve;: &auml;&acirc;&agrave; &auml;&aring;&ntilde;&yuml;&ograve;&ecirc;&agrave;
&oacute;&igrave;&iacute;&icirc;&aelig;&egrave;&ograve;&uuml; &iacute;&agrave; &ograve;&eth;&egrave; &auml;&aring;&ntilde;&yuml;&ograve;&ecirc;&agrave;?
2. &Icirc;&auml;&iacute;&icirc; &yuml;&eacute;&ouml;&icirc; &acirc;&agrave;&eth;&yuml;&ograve; &ograve;&eth;&egrave; &igrave;&egrave;&iacute;&oacute;&ograve;&ucirc;.
&Ntilde;&ecirc;&icirc;&euml;&uuml;&ecirc;&icirc; &igrave;&egrave;&iacute;&oacute;&ograve; &iacute;&agrave;&auml;&icirc; &acirc;&agrave;&eth;&egrave;&ograve;&uuml; 5 &yuml;&egrave;&ouml;?
&ecirc;&eth;&agrave;&ntilde;&iacute;&ucirc;&otilde; &ecirc;&icirc;&euml;&icirc;&iacute;&ecirc;&agrave;&otilde; &eth;&agrave;&ntilde;&iuml;&icirc;&euml;&icirc;&aelig;&aring;&iacute;&ucirc;
&divide;&egrave;&ntilde;&euml;&icirc;&acirc;&ucirc;&aring; &iuml;&icirc;&ntilde;&euml;&aring;&auml;&icirc;&acirc;&agrave;&ograve;&aring;&euml;&uuml;&iacute;&icirc;&ntilde;&ograve;&egrave;, &ntilde;&acirc;&yuml;-
5 + 8 + 9 + 8 + 5 = 1 5 + 2 4 + 3 3 + 4 2 + 5 1=
&ETH;&egrave;&ntilde;.6
=
+
+
+
+
=
&ETH;&egrave;&ntilde;.10
&ccedil;&agrave;&iacute;&iacute;&ucirc;&aring; &ntilde; &ograve;&eth;&aring;&oacute;&atilde;&icirc;&euml;&uuml;&iacute;&ucirc;&igrave;&egrave; &divide;&egrave;&ntilde;&euml;&agrave;&igrave;&egrave;, &agrave;
&acirc; &ntilde;&egrave;&iacute;&egrave;&otilde; &ecirc;&icirc;&euml;&icirc;&iacute;&ecirc;&agrave;&otilde;  &ntilde; &ecirc;&acirc;&agrave;&auml;&eth;&agrave;&ograve;&iacute;&ucirc;&igrave;&egrave;
&divide;&egrave;&ntilde;&euml;&agrave;&igrave;&egrave;. &Iuml;&icirc;&iuml;&eth;&icirc;&aacute;&oacute;&eacute;&ograve;&aring; &oacute;&ntilde;&ograve;&agrave;&iacute;&icirc;&acirc;&egrave;&ograve;&uuml;
&yacute;&ograve;&oacute; &ntilde;&acirc;&yuml;&ccedil;&uuml; &ntilde;&agrave;&igrave;&icirc;&ntilde;&ograve;&icirc;&yuml;&ograve;&aring;&euml;&uuml;&iacute;&icirc;.
&Atilde;&eth;&oacute;&iuml;&iuml;&ucirc; &divide;&egrave;&ntilde;&aring;&euml; 1; 2,2; 3,4,3;
4,6,6,4;  &iacute;&agrave;&ccedil;&icirc;&acirc;&aring;&igrave; &ntilde;&ograve;&eth;&icirc;&ecirc;&agrave;&igrave;&egrave; &eth;&agrave;&ntilde;&oslash;&egrave;&eth;&aring;&iacute;&iacute;&icirc;&eacute; &ograve;&agrave;&aacute;&euml;&egrave;&ouml;&ucirc; &Iuml;&egrave;&ocirc;&agrave;&atilde;&icirc;&eth;&agrave;
(&eth;&egrave;&ntilde;.9). &Iuml;&eth;&icirc;&egrave;&ccedil;&acirc;&aring;&auml;&aring;&iacute;&egrave;&aring; &divide;&egrave;&ntilde;&aring;&euml; n-&eacute;
2
&ntilde;&ograve;&eth;&icirc;&ecirc;&egrave; &eth;&agrave;&acirc;&iacute;&icirc; n! , &iuml;&icirc;&ograve;&icirc;&igrave;&oacute; &divide;&ograve;&icirc;
&divide;&egrave;&ntilde;&euml;&agrave; &yacute;&ograve;&icirc;&eacute; &ntilde;&ograve;&eth;&icirc;&ecirc;&egrave; &igrave;&icirc;&aelig;&iacute;&icirc; &iuml;&eth;&aring;&auml;&ntilde;&ograve;&agrave;&acirc;&egrave;&ograve;&uuml; &acirc; &ograve;&agrave;&ecirc;&icirc;&igrave;
2 n −1 ,
&acirc;&egrave;&auml;&aring;:
1n,
3 n − 2 , ,
n −2 3,
n − 1 2 , n1, &agrave; &iuml;&eth;&icirc;&egrave;&ccedil;&acirc;&aring;&auml;&aring;&iacute;&egrave;&aring; &ograve;&agrave;&ecirc;&egrave;&otilde; &divide;&egrave;&ntilde;&aring;&euml; &eth;&agrave;&acirc;&iacute;&icirc;
2
n! .
&Ntilde;&oacute;&igrave;&igrave;&agrave; &divide;&egrave;&ntilde;&aring;&euml; n-&eacute; &ntilde;&ograve;&eth;&icirc;&ecirc;&egrave; &ograve;&agrave;&aacute;&euml;&egrave;&ouml;&ucirc; &Iuml;&egrave;&ocirc;&agrave;&atilde;&icirc;&eth;&agrave;
&eth;&agrave;&acirc;&iacute;&agrave; n-&igrave;&oacute; &ograve;&aring;&ograve;&eth;&agrave;&yacute;&auml;&eth;&agrave;&euml;&uuml;&iacute;&icirc;&igrave;&oacute; &divide;&egrave;&ntilde;&euml;&oacute; &egrave; &igrave;&icirc;&aelig;&aring;&ograve;
&aacute;&ucirc;&ograve;&uuml; &acirc;&ucirc;&divide;&egrave;&ntilde;&euml;&aring;&iacute;&agrave; &iuml;&icirc; &ocirc;&icirc;&eth;-
&gt; C
&gt;
&gt; C
&gt; C
&ETH;&egrave;&ntilde;.7
C&gt;
24
&gt;
&iacute;&agrave; &iuml;&icirc;&ntilde;&euml;&aring;&auml;&icirc;&acirc;&agrave;&ograve;&aring;&euml;&uuml;&iacute;&icirc;&ntilde;&ograve;&uuml; &ecirc;&acirc;&agrave;&auml;&eth;&agrave;&ograve;&iacute;&ucirc;&otilde;
&divide;&egrave;&ntilde;&aring;&euml;, &agrave; &iuml;&agrave;&eth;&agrave;&euml;&euml;&aring;&euml;&uuml;&iacute;&icirc; &egrave; &eth;&yuml;&auml;&icirc;&igrave; &ntilde; &iacute;&aring;&eacute;
&eth;&agrave;&ntilde;&iuml;&icirc;&euml;&icirc;&aelig;&aring;&iacute;&ucirc; &oacute;&auml;&acirc;&icirc;&aring;&iacute;&iacute;&ucirc;&aring; &ograve;&eth;&aring;&oacute;&atilde;&icirc;&euml;&uuml;&iacute;&ucirc;&aring; &divide;&egrave;&ntilde;&euml;&agrave;. (&Iacute;&agrave;&iuml;&icirc;&igrave;&iacute;&egrave;&igrave;, &divide;&ograve;&icirc; &ograve;&eth;&aring;&oacute;&atilde;&icirc;&euml;&uuml;&iacute;&ucirc;&igrave;&egrave; &iacute;&agrave;&ccedil;&ucirc;&acirc;&agrave;&thorn;&ograve; &divide;&egrave;&ntilde;&euml;&agrave;, &iuml;&icirc;&ecirc;&agrave;&ccedil;&ucirc;&acirc;&agrave;&thorn;&ugrave;&egrave;&aring;, &egrave;&ccedil; &ntilde;&ecirc;&icirc;&euml;&uuml;&ecirc;&egrave;&otilde; &ecirc;&eth;&oacute;&atilde;&icirc;&acirc;
&igrave;&icirc;&aelig;&iacute;&icirc; &ntilde;&euml;&icirc;&aelig;&egrave;&ograve;&uuml; &ograve;&eth;&aring;&oacute;&atilde;&icirc;&euml;&uuml;&iacute;&egrave;&ecirc;: 1, 3,
9 18 27 36 45 54 63 72 81
&igrave;&icirc;&aelig;&iacute;&icirc; &eth;&agrave;&ntilde;&oslash;&egrave;&eth;&egrave;&ograve;&uuml; &acirc;&iuml;&eth;&agrave;&acirc;&icirc; &egrave; &acirc;&iacute;&egrave;&ccedil;,
&ntilde;&icirc;&aacute;&euml;&thorn;&auml;&agrave;&yuml; &icirc;&ntilde;&iacute;&icirc;&acirc;&iacute;&icirc;&aring; &oacute;&ntilde;&euml;&icirc;&acirc;&egrave;&aring;: &ecirc;&agrave;&aelig;&auml;&icirc;&aring; &divide;&egrave;&ntilde;&euml;&icirc; &ograve;&agrave;&aacute;&euml;&egrave;&ouml;&ucirc; &aring;&ntilde;&ograve;&uuml; &iuml;&eth;&icirc;&egrave;&ccedil;&acirc;&aring;&auml;&aring;&iacute;&egrave;&aring; &iacute;&icirc;&igrave;&aring;&eth;&agrave; &ntilde;&ograve;&eth;&icirc;&ecirc;&egrave; &egrave; &iacute;&icirc;&igrave;&aring;&eth;&agrave; &ntilde;&ograve;&icirc;&euml;&aacute;&ouml;&agrave;, &acirc; &ecirc;&icirc;&ograve;&icirc;&eth;&ucirc;&otilde; &icirc;&iacute;&icirc; &ntilde;&ograve;&icirc;&egrave;&ograve;. &Iacute;&agrave; &eth;&egrave;&ntilde;&oacute;&iacute;&ecirc;&aring; 7 &egrave;&ccedil;&icirc;&aacute;&eth;&agrave;&aelig;&aring;&iacute;&agrave; &acirc;&aring;&eth;&otilde;&iacute;&yuml;&yuml; &divide;&agrave;&ntilde;&ograve;&uuml;
&eth;&agrave;&ntilde;&oslash;&egrave;&eth;&aring;&iacute;&iacute;&icirc;&eacute; &ograve;&agrave;&aacute;&euml;&egrave;&ouml;&ucirc; &Iuml;&egrave;&ocirc;&agrave;&atilde;&icirc;&eth;&agrave;,
&iuml;&icirc;&acirc;&aring;&eth;&iacute;&oacute;&ograve;&agrave;&yuml; &iacute;&agrave; 45&deg;. &Aring;&ntilde;&ograve;&aring;&ntilde;&ograve;&acirc;&aring;&iacute;&iacute;&icirc;,
&acirc;&ntilde;&aring; &eth;&agrave;&iacute;&aring;&aring; &ntilde;&ocirc;&icirc;&eth;&igrave;&oacute;&euml;&egrave;&eth;&icirc;&acirc;&agrave;&iacute;&iacute;&ucirc;&aring; &ntilde;&acirc;&icirc;&eacute;&ntilde;&ograve;&acirc;&agrave; &ograve;&agrave;&aacute;&euml;&egrave;&ouml;&ucirc; &Iuml;&egrave;&ocirc;&agrave;&atilde;&icirc;&eth;&agrave; &icirc;&ntilde;&ograve;&agrave;&thorn;&ograve;&ntilde;&yuml;
&acirc;&aring;&eth;&iacute;&ucirc;&igrave;&egrave; &egrave; &auml;&euml;&yuml; &eth;&agrave;&ntilde;&oslash;&egrave;&eth;&aring;&iacute;&iacute;&icirc;&eacute; &ograve;&agrave;&aacute;&euml;&egrave;&ouml;&ucirc;, &iuml;&icirc;&yacute;&ograve;&icirc;&igrave;&oacute; &acirc; &auml;&agrave;&euml;&uuml;&iacute;&aring;&eacute;&oslash;&aring;&igrave; &eth;&agrave;&ntilde;&oslash;&egrave;&eth;&aring;&iacute;&iacute;&oacute;&thorn; &ograve;&agrave;&aacute;&euml;&egrave;&ouml;&oacute; &ograve;&agrave;&ecirc;&aelig;&aring; &aacute;&oacute;&auml;&aring;&igrave;
&iacute;&agrave;&ccedil;&ucirc;&acirc;&agrave;&ograve;&uuml; &ograve;&agrave;&aacute;&euml;&egrave;&ouml;&aring;&eacute; &Iuml;&egrave;&ocirc;&agrave;&atilde;&icirc;&eth;&agrave;.
&ETH;&agrave;&ntilde;&ntilde;&igrave;&icirc;&ograve;&eth;&egrave;&igrave; &ecirc;&icirc;&euml;&icirc;&iacute;&ecirc;&egrave; &divide;&egrave;&ntilde;&aring;&euml;, &eth;&agrave;&ntilde;&iuml;&icirc;&euml;&icirc;&aelig;&aring;&iacute;&iacute;&ucirc;&otilde; &iuml;&agrave;&eth;&agrave;&euml;&euml;&aring;&euml;&uuml;&iacute;&icirc; &aacute;&egrave;&ntilde;&ntilde;&aring;&ecirc;&ograve;&eth;&egrave;&ntilde;&aring; &laquo;&divide;&egrave;&ntilde;&euml;&icirc;&acirc;&icirc;&atilde;&icirc; &oacute;&atilde;&euml;&agrave;&raquo; (&eth;&egrave;&ntilde;.8).
&Iacute;&agrave; &ntilde;&agrave;&igrave;&icirc;&eacute; &aacute;&egrave;&ntilde;&ntilde;&aring;&ecirc;&ograve;&eth;&egrave;&ntilde;&aring; &eth;&agrave;&ntilde;&iuml;&icirc;&euml;&icirc;&aelig;&aring;-
C&gt;
&oacute;&atilde;&icirc;&euml;&uuml;&iacute;&ucirc;&otilde; &divide;&egrave;&ntilde;&aring;&euml; &auml;&euml;&yuml; &iuml;&eth;&icirc;&ntilde;&ograve;&eth;&agrave;&iacute;&ntilde;&ograve;&acirc;&agrave;
&divide;&aring;&ograve;&ucirc;&eth;&aring;&otilde; &egrave;&ccedil;&igrave;&aring;&eth;&aring;&iacute;&egrave;&eacute;).
&Ecirc;&agrave;&ecirc; &acirc;&ucirc; &oacute;&aelig;&aring; &oacute;&ntilde;&iuml;&aring;&euml;&egrave;, &iacute;&agrave;&acirc;&aring;&eth;&iacute;&icirc;&aring;,
&ccedil;&agrave;&igrave;&aring;&ograve;&egrave;&ograve;&uuml;, &acirc; &ntilde;&acirc;&icirc;&eacute;&ntilde;&ograve;&acirc;&agrave;&otilde; &yacute;&ograve;&icirc;&eacute; &ograve;&agrave;&aacute;&euml;&egrave;&ouml;&ucirc; &ograve;&aring;&ntilde;&iacute;&icirc; &iuml;&aring;&eth;&aring;&iuml;&euml;&aring;&ograve;&agrave;&thorn;&ograve;&ntilde;&yuml; &ograve;&eth;&aring;&oacute;&atilde;&icirc;&euml;&uuml;&iacute;&ucirc;&aring; &egrave; &ecirc;&acirc;&agrave;&auml;&eth;&agrave;&ograve;&iacute;&ucirc;&aring; &divide;&egrave;&ntilde;&euml;&agrave;. &Acirc;&icirc;&ograve; &aring;&ugrave;&aring;
&icirc;&auml;&iacute;&icirc; &ntilde;&acirc;&icirc;&eacute;&ntilde;&ograve;&acirc;&icirc;: &eth;&agrave;&ccedil;&iacute;&icirc;&ntilde;&ograve;&uuml; &igrave;&aring;&aelig;&auml;&oacute; &ntilde;&oacute;&igrave;&igrave;&agrave;&igrave;&egrave; n-&eacute; &egrave; n − 1 -&eacute; &ntilde;&ograve;&eth;&icirc;&ecirc; &ograve;&agrave;&aacute;&euml;&egrave;&ouml;&ucirc;
&eth;&agrave;&acirc;&iacute;&agrave; n-&igrave;&oacute; &ograve;&eth;&aring;&oacute;&atilde;&icirc;&euml;&uuml;&iacute;&icirc;&igrave;&oacute; &divide;&egrave;&ntilde;&euml;&oacute;, &agrave;
&eth;&agrave;&ccedil;&iacute;&icirc;&ntilde;&ograve;&uuml; &igrave;&aring;&aelig;&auml;&oacute; &ntilde;&oacute;&igrave;&igrave;&agrave;&igrave;&egrave; n-&eacute; &egrave;
n − 2 -&eacute; &ntilde;&ograve;&eth;&icirc;&ecirc; &eth;&agrave;&acirc;&iacute;&agrave; n-&igrave;&oacute; &ecirc;&acirc;&agrave;&auml;&eth;&agrave;&ograve;&iacute;&icirc;&igrave;&oacute; &divide;&egrave;&ntilde;&euml;&oacute;.
&ETH;&egrave;&ntilde;.5
1 2
C . (&Ograve;&aring;&ograve;&eth;&agrave;&yacute;&auml;&eth;&agrave;&euml;&uuml;-
n n +1 n +2 n + 3
9 18 27 36 45 54 63 72 81
&acirc;&agrave;&ograve;&aring;&euml;&uuml;&iacute;&icirc;&ntilde;&ograve;&uuml; &ecirc;&oacute;&aacute;&icirc;&acirc; &iacute;&agrave;&ograve;&oacute;&eth;&agrave;&euml;&uuml;&iacute;&ucirc;&otilde;
&divide;&egrave;&ntilde;&aring;&euml;.
&Iacute;&aring; &iacute;&agrave;&eth;&oacute;&oslash;&agrave;&yuml; &iuml;&eth;&egrave;&iacute;&ouml;&egrave;&iuml;&egrave;&agrave;&euml;&uuml;&iacute;&icirc;&atilde;&icirc;
&iuml;&icirc;&ntilde;&ograve;&eth;&icirc;&aring;&iacute;&egrave;&yuml; &ograve;&agrave;&aacute;&euml;&egrave;&ouml;&ucirc; &Iuml;&egrave;&ocirc;&agrave;&atilde;&icirc;&eth;&agrave;, &aring;&aring;
C&gt;
6
&iacute;&ucirc;&igrave;&egrave; &divide;&egrave;&ntilde;&euml;&agrave;&igrave;&egrave; &iacute;&agrave;&ccedil;&ucirc;&acirc;&agrave;&thorn;&ograve; &divide;&egrave;&ntilde;&euml;&agrave;,
&iuml;&icirc;&ecirc;&agrave;&ccedil;&ucirc;&acirc;&agrave;&thorn;&ugrave;&egrave;&aring;, &egrave;&ccedil; &ntilde;&ecirc;&icirc;&euml;&uuml;&ecirc;&egrave;&otilde; &oslash;&agrave;&eth;&icirc;&acirc; &igrave;&icirc;&aelig;&iacute;&icirc; &ntilde;&euml;&icirc;&aelig;&egrave;&ograve;&uuml; &ograve;&eth;&aring;&oacute;&atilde;&icirc;&euml;&uuml;&iacute;&oacute;&thorn;
&iuml;&egrave;&eth;&agrave;&igrave;&egrave;&auml;&oacute;.) &Iacute;&agrave; &eth;&egrave;&ntilde;&oacute;&iacute;&ecirc;&aring; 10 &iuml;&icirc;&ecirc;&agrave;&ccedil;&agrave;&iacute; &iuml;&eth;&icirc;&ouml;&aring;&ntilde;&ntilde; &eth;&icirc;&aelig;&auml;&aring;&iacute;&egrave;&yuml; &ograve;&aring;&ograve;&eth;&agrave;&yacute;&auml;&eth;&agrave;&euml;&uuml;&iacute;&icirc;&atilde;&icirc; &divide;&egrave;&ntilde;&euml;&agrave; &egrave;&ccedil; &divide;&egrave;&ntilde;&aring;&euml; 5-&eacute; &ntilde;&ograve;&eth;&icirc;&ecirc;&egrave;.
&Ntilde;&oacute;&igrave;&igrave;&agrave; &aelig;&aring; &acirc;&ntilde;&aring;&otilde; &divide;&egrave;&ntilde;&aring;&euml; n &iuml;&aring;&eth;&acirc;&ucirc;&otilde;
&ntilde;&ograve;&eth;&icirc;&ecirc; &ograve;&agrave;&aacute;&euml;&egrave;&ouml;&ucirc; &eth;&agrave;&acirc;&iacute;&agrave; n-&igrave;&oacute; &atilde;&egrave;&iuml;&aring;&eth;&ograve;&aring;&ograve;&eth;&agrave;&yacute;&auml;&eth;&agrave;&euml;&uuml;&iacute;&icirc;&igrave;&oacute;
&divide;&egrave;&ntilde;&euml;&oacute;
5 10 15 20 25 30 35 40 45
6 12 18 24 30 36 42 48 54
&gt;
n n +1 n + 2
C
&gt;
&gt;
C
C
3. &Iacute;&agrave; &auml;&icirc;&ntilde;&ecirc;&aring; &iacute;&agrave;&iuml;&egrave;&ntilde;&agrave;&iacute;&icirc; &iacute;&aring;&ntilde;&ecirc;&icirc;&euml;&uuml;&ecirc;&icirc;
&iuml;&euml;&thorn;&ntilde;&icirc;&acirc; &egrave; &igrave;&egrave;&iacute;&oacute;&ntilde;&icirc;&acirc;. &ETH;&agrave;&ccedil;&eth;&aring;&oslash;&agrave;&aring;&ograve;&ntilde;&yuml;
&ntilde;&ograve;&egrave;&eth;&agrave;&ograve;&uuml; &euml;&thorn;&aacute;&ucirc;&aring; &auml;&acirc;&agrave; &ccedil;&iacute;&agrave;&ecirc;&agrave;, &ccedil;&agrave;&iuml;&egrave;&ntilde;&ucirc;&acirc;&agrave;&yuml; &acirc;&igrave;&aring;&ntilde;&ograve;&icirc; &icirc;&auml;&egrave;&iacute;&agrave;&ecirc;&icirc;&acirc;&ucirc;&otilde; &ccedil;&iacute;&agrave;&ecirc;&icirc;&acirc;
&iuml;&euml;&thorn;&ntilde;, &agrave; &acirc;&igrave;&aring;&ntilde;&ograve;&icirc; &eth;&agrave;&ccedil;&iacute;&ucirc;&otilde;  &igrave;&egrave;&iacute;&oacute;&ntilde;.
&Ccedil;&agrave;&acirc;&egrave;&ntilde;&egrave;&ograve; &euml;&egrave; &iuml;&icirc;&ntilde;&euml;&aring;&auml;&iacute;&egrave;&eacute; &icirc;&ntilde;&ograve;&agrave;&acirc;&oslash;&egrave;&eacute;&ntilde;&yuml;
&iacute;&agrave; &auml;&icirc;&ntilde;&ecirc;&aring; &ccedil;&iacute;&agrave;&ecirc; &icirc;&ograve; &ograve;&icirc;&atilde;&icirc;, &acirc; &ecirc;&agrave;&ecirc;&icirc;&igrave;
&iuml;&icirc;&eth;&yuml;&auml;&ecirc;&aring; &ntilde;&ograve;&egrave;&eth;&agrave;&ograve;&uuml; &ccedil;&iacute;&agrave;&ecirc;&egrave;?
&Iacute;.&Agrave;&acirc;&egrave;&euml;&icirc;&acirc;
```