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

来源：学生作业帮编辑：神马作文网作业帮分类：数学作业时间：2024/11/18 08:58:06

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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