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1/X(X+1)+1/(X+1)(X+2)+1/(X+2)(X+3).+1/(X+99)(X+100)=

来源:学生作业帮 编辑:作业帮 分类:数学作业 时间:2024/05/16 13:58:39
1/X(X+1)+1/(X+1)(X+2)+1/(X+2)(X+3).+1/(X+99)(X+100)=
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)