1/(x+1)(x+2)+1/(x+2)(x+3)+…+1/(x+99)(x+100)

1/(x+1)(x+2)+1/(x+2)(x+3)+…+1/(x+99)(x+100)

题目
1/(x+1)(x+2)+1/(x+2)(x+3)+…+1/(x+99)(x+100)
答案
1/x(x+1)+1/(x+1)(x+2)+1/(x+2)(x+3)+.+1/(x+99)(x+100)
=1/x-1/(x+1)+1/(x+1)-1/(x+2)+1/(x+2)-1/(x+3)+.+1/(x+99)-1/(x+100)
=1/x-1/(x+100)
=100/[x(x+100)]
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