(1*5)分之1+(5*9)分之1+(9*13)分之1+……+(101*105)分之1=?

问题描述:

(1*5)分之1+(5*9)分之1+(9*13)分之1+……+(101*105)分之1=?

1/4(1-1/5 1/5-1/9 1/9-1/13 …… 1/101-1/105)=1/4(1-1/105),自己来吧

(1*5)分之1+(5*9)分之1+(9*13)分之1+……+(101*105)分之1
=1/4*(1-1/5)+1/4*(1/5-1/9)+1/4*(1/9-1/13)+……+1/4*(1/97-1/101)+1/4*(1/101-1/105)
=1/4*(1-1/5+1/5-1/9+1/9-1/13+……+1/97-1/101+1/101-1/105)
=1/4*(1-1/105)
=26/105

1/4[(1/1-1/5)+(1/5-1/9)+...+1/101-1/105)]
=1/4*104/105
=26/105