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

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

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