解一下这道题1/5X9+1/9X13+1/13X17+...1/101X105=?
问题描述:
解一下这道题1/5X9+1/9X13+1/13X17+...1/101X105=?
答
1/5X9+1/9X13+1/13X17+...1/101X105=(1/4)*(1/5-1/9)+(1/4)*(1/9-1/13)+(1/4)*(1/13-1/17)+.+(1/4)*(1/101-1/105)=(1/4)*(1/5-1/9+1/9-1/13+1/13-1/17+.+1/101-1/105)=(1/4)*(1/5-1/105)=(1/4)*(4/21)=1/21