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:2024/07/06 01:27:21
![1+ 1/1 +2+ 1/1+2+3 + 1/1+2+3+4 +``````+ 1/1+2+3+```+200](/uploads/image/z/4343842-10-2.jpg?t=1%2B+1%2F1+%2B2%2B+1%2F1%2B2%2B3+%2B+1%2F1%2B2%2B3%2B4+%2B%60%60%60%60%60%60%2B+1%2F1%2B2%2B3%2B%60%60%60%2B200)
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