计算1/X(X+1)+1/(X+1)(X+2)+.+1/(X+99)(X+100)

问题描述:

计算1/X(X+1)+1/(X+1)(X+2)+.+1/(X+99)(X+100)
1个回答 分类:数学 2014-10-23

问题解答:

我来补答
1/X(X+1)+1/(X+1)(X+2)+.+1/(X+99)(X+100)
=[1/x - 1/(x+1)] +[1/(x+1) - 1/(x+2) ]+.+[1/(x+99) - 1/(x+100)]
=1/x - 1//(x+100)
=100/x(x+100)
 
 
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