1x1+2x2+3x3......20000x20000=?
2009-10-02 7:06 pm
1x1 + 2x2 + 3x3 + 4x4 + 5x5 + 6x6 + 7x7 + 8x8 + 9x9 + 10x10 ...... + 20000x20000 = ??
回答 (1)
2009-10-03 1:28 am
✔ 最佳答案
平方和 1^2 + 2^2 + 3^2 + 4^2 + ...... + N^2 的求和公式 :N(N + 1)(2N + 1) / 6
所以 1x1 + 2x2 + 3x3 + 4x4 + 5x5 + 6x6 + 7x7 + 8x8 + 9x9 + 10x10 ...... + 20000x20000
= 1^2 + 2^2 + 3^2 + 4^2 + ... + 20000^2
= 20000(20000+1)(2 * 20000 + 1) / 6
= 20000(20001)(40001) / 6
= [2 * 20001 * 40001 / 6] * 10000
= 2666866670000
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原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20091002000051KK00411