学生升降桌的厂家电话:1/(1*3)+1/(3*5) ........+1/(99*101)

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我要过程

1/n*(n+2)=1/2n-1/2(n+2),所以原式=0.5{1-1/3+1/3-1/5~~~~~~-1/101}=100/202

1/(1*3)+1/(3*5) ........+1/(99*101)

=1/2*(1-1/3)+2*(1/3-1/5).....+2*(1/99-1/101)
=1/2*(1-1/3+1/3-1/5+1/5-1/7......-1/99+1/99-1/101)
=1/2*(1-1/101)
=100/202