1/1乘5+1/5乘9+1/9乘13……+1/101乘105怎么算?
问题描述：
1/1乘5+1/5乘9+1/9乘13……+1/101乘105怎么算?
答
裂项1/[n(n+4)]=[1/n-1/(n+4)]*1/4
所以1/(1*5)+...+1/(101*105)
=1/4*(1-1/5+1/5-1/9+....+1/101+1/105)
=1/4*(1-1/105)
=1/4*104/105
=26/105
答
1/1x5+1/5x9+1/9x13……+1/101x105=1/4(1-1/5+1/5-1/9+1/9-1/13+……+1/101-1/105)=1/4(1-1/105)=1/4 x 104/105=26/105【1/n(n+m)=1/m x (1/n-1/(n+m))】希望能够帮到你,祝你学习愉快!