• 所有问题

    • 1x2+2x3+3x4+4x5+···n（n+1）=_____（n为自然数）

    今晚要

    举报该问题
    推荐答案   2013-10-21
    n(n+1)=n^2+nS(n)=(1+2^2+3^2+...+n^2)+(1+2+3+...+n)

    =n(n+1)(2n+1)/6+n(n+1)/2

    =n(n+1)(2n+1+3)/6

    =n(n+1)(n+2)/3
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