, .

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18.03.2013

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(an) = 5n2 - 2.

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ak ak+1. , , (?):

5k2 - 2 (?) 5(k + 1)2 - 2;

5k2 - 2 (?) 5(k2 + 2k + 1) - 2;

5k2 - 2 (?) 5k2 + 10k +3;

0 (?) 10k + 5;

, k ≥ 1, 0 k. ak+1 > ak k, , , , .

: , .


(an) = n2 + 3n + 2.

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, n2 + 3n + 2 = (n + 1)(n + 2). ak, ak+1 :

(k + 1)(k + 2) (?) (k + 2)(k + 3);

0 (?) (k + 2)(k + 3) - (k + 1)(k + 2);

0 (?) 2(k + 2);

0 (?) k + 2.

, ak+1ak k ≥ -2 ( ) - , .

: , .


(an) = n2 - 11n + 30.

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, n2 - 11n + 30 = (n - 5)(n - 6). ak ak+1:

(k - 5)(k - 6) (?) (k - 4)(k - 5);

0 (?) (k - 4)(k - 5) - (k - 5)(k - 6);

0 (?) 2(k - 5);

5 (?) k.

ak+1ak k ≥ 5, ak+1 < ak k < 5. .

: .


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