(1x3)分之1 + (3x5)分之1+ (5x7)分之1 + (7x9)分之1 +(9x11)分之1

问题描述:

(1x3)分之1 + (3x5)分之1+ (5x7)分之1 + (7x9)分之1 +(9x11)分之1

1-3分之1+3分之一。。。。。。。-11分之一。【应该没错。。】

1/(1×3)+1/(3×5)+1/(5×7)+1/(7×9)+1/(9×11)
=(1-1/3)/2+(1/3-1/5)/2+(1/5-1/7)/2+(1/7-1/9)/2+(1/9-1/11)/2.
=(1-1/3+1/3-1/5+1/5-1/7+1/7-1/9+1/9-1/11)/2
=(1-1/11)/2
=(10/11)/2
=5/11