一定要帮我啊!(1/1x2)+(1/2x3)+(1/3x4)+(1/4x5)+.+(1/99x100)=?
问题描述：
一定要帮我啊!(1/1x2)+(1/2x3)+(1/3x4)+(1/4x5)+.+(1/99x100)=?
答
1/[n*(n+1)]=1/n-1/(n+1)
(1/1x2)+(1/2x3)+(1/3x4)+(1/4x5)+.....+(1/99x100)=(1-1/2)+(1/2-1/3)+......+(1/99-1/100)
=1-1/100=0.99
答
因为
1/1×2 = 1 - 1/2
1/2×3 = 1/2 - 1/3
依此类推
1/99×100 = 1/99 - 1/100
所以
原式 = 1 - 1/2 + 1/2 - 1/3 + 1/3 - 1/4 + ...+ 1/99 - 1/00
= 1 - 1/100
= 99/100