1/3-2/15+3/35-4/63+5/99-6/143=?分数简便计算

1/3-2/15+3/35-4/63+5/99-6/143=[1/3-2/(3×5)]+[3/(5×7)-4/(7×9)]+[5/(9×11)-6/(11×13)]=1/3×（1-2/5）+1/7×（3/5-4/9）+1/11×（5/9-6/13）=1/3×3/5+1/7×7/45+1/11×11/117=1/5+1/45+1/117=2/9+1/117=1/9...