3^2+6^2+9^2+...+30^2.

👨🏻‍🏫 學術台數學

kelly

2010-07-17 4:23 am

(a) prove by mathematical induction that 1^2 +2^2 +3^2 +...+n^2
=n(n+1)(2n+1)/6

(b) hence, evaluate 3^2+6^2+9^2+...+30^2.

我識做a ,但係吾識點運用到a去做b,,所以淨係做b就得嫁啦

回答 (4)

用戶10012

2010-07-17 4:44 am

✔ 最佳答案

3^2 + 6^2 + 9^2 + ...... + 30^2
= (3 x 1)^2 + (3 x 2)^2 + (3 x 3)^2 + ....... + ( 3 x 10)^2
= 3^2[1^2 + 2^2 + 3^2 + .... + 10^2]
= (9)(10)(10 + 1)(20 + 1)/6 = (9)(10)(11)(21)/6 = (3)(5)(11)(21) = 3465.

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知識就是力量

2010-07-17 6:03 am

(b) 將每個term抽3^2出黎 done

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