1/9x11+1/11x13+1/13x15+……+1/43x45=

silverbox2022-10-04 11:39:541条回答

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fffxxxhhh007 共回答了17个问题 | 采纳率100%: 1/(9×11)+1/(11×13)+1/(13×15)+...+1/(43×45)
=(1/2)(1/9-1/11+1/11-1/13+1/13-1/15+...+1/43-1/45)
=(1/2)(1/9-1/45)
=2/45
一般的：1/[n(n+2)]=(1/2)[1/n -1/(n+1)]
1/[n(n+k)]=(1/k)[1/n -1/(n+k)]; 1年前

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