3分子1加15分子1加35分之1加63分之一加99分之一加143分子1的简便计算

1/3+1/15+1/35+1/63+1/99+1/143=1/3+1/(3*5)+1/(5*7)+1/(7*9)+1/(9*11)+1/(11*13)
=1/3+(1/3-1/5+1/5-1/7+1/7-1/9+1/9-1/11+1/11-1/13)/2
=1/3+(1/3-1/13)/2
=1/3+1/6-1/26
=1/2-1/26
=6/13