Question

求1/(1*3*5)+1/(3*5*7)+1/(5*7*9)+1/(7*9*11)的简便算法

Answer 1

1/(1*3*5)+1/(3*5*7)+1/(5*7*9)+1/(7*9*11)

=1/4(1/1*3-1/3*5)+1/4(1/3*5-1/5*7)+1/4(1/5*7-1/7*9)+1/4(1/7*9-1/9*11)

=1/4×1/1*3 - 1/4×1/9*11

=8/99