求1x2,2x3,3x4,4x5.99x100.前99项的倒数之和.

问题描述:

求1x2,2x3,3x4,4x5.99x100.前99项的倒数之和.

1/(1x2)=1/1-1/2
1/(2x3)=1/2-1/3
1/(3x4)=1/3-1/4
.
1/(98x99)=1/98-1/99
1/(99x100)=1/99-1/100
之和为1/1-1/100=99/100