若n为正整数,求1/n(n+1)+1/(n+1)(n+2)＋1/(n+2)(n+3)+1/(n+3)(n+4)+.+1/

学习时间:2026-03-29 17:51:34 阅读：5368

若n为正整数,求1/n(n+1)+1/(n+1)(n+2)＋1/(n+2)(n+3)+1/(n+3)(n+4)+.+1/(n+99)(n+100)的值观察算式1/1X2=1-1/2 1/1x2+1/2x3=1-1/2+1/2-1/3=2/3.

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2026-03-29 17:51:34

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1/n(n+1)+1/(n+1)(n+2)＋1/(n+2)(n+3)+1/(n+3)(n+4)+。+1/(n+99)(n+100)=1/n-1/(n+1)+1/(n+1)-1/(n+2)+。。。+1/(n+99)-1/(n+100)=1/n-1/(n+100)=100/n(n+100)