1/3+1/15+1/35+1/63+1/99+1/143的简便算法（写过程）

题目

1/3+1/15+1/35+1/63+1/99+1/143的简便算法（写过程）

答案

原式=1/1*3+1/(3*5)+1/(5*7)+1/(7*9)+1/(9*11)+1/(11*13)
=1/2(1-1/3)+1/2(1/3-1/5)+1/2(1/5-1/7)+1/2(1/7-1/9)+1/2(1/9-1/11)+1/2(1/11-1/13)
=1/2(1-1/13)=6/13