1+ 1/1 +2+ 1/1+2+3 + 1/1+2+3+4 +``````+ 1/1+2+3+```+200

来源：学生作业帮助网 编辑：作业帮 时间：2024/07/05 10:53:22
1+ 1/1 +2+ 1/1+2+3 + 1/1+2+3+4 +``````+ 1/1+2+3+```+200
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1+ 1/1 +2+ 1/1+2+3 + 1/1+2+3+4 +``````+ 1/1+2+3+```+200
1+ 1/1 +2+ 1/1+2+3 + 1/1+2+3+4 +``````+ 1/1+2+3+```+200

1+ 1/1 +2+ 1/1+2+3 + 1/1+2+3+4 +``````+ 1/1+2+3+```+200
1+2+……+n=n(n+1)/2
所以1/(1+2+……+n)=2/n(n+1)=2[1/n-1/(n+1)]
所以原式=2[(1-1/2)+(1/2-1/3)+……+(1/200+1/201)]
=2(1-1/201)
=400/201