1+1/2+1/6+1/12+20/1+30/1+42/1+56/1+...+1/132

1+1/2+1/6+1/12+20/1+30/1+42/1+56/1+...+1/132
1+1/2+1/6+1/12+20/1+30/1+42/1+56/1+...+1/132

1+1/2+1/6+1/12+20/1+30/1+42/1+56/1+...+1/132
裂项法
原式=1+1/(1*2)+1/(2*3)+1/(3*4)+...+1/(11*12)
=1+1-1/2+1/2-1/3+1/3-1/4+...+1/11-1/12
=2-1/12=23/12

1+1/2+1/6+1/12+1/20+1/30+1/42+1/56+...+1/132
=1+1/1*2+1/2*3+1/3*4+……+1/11*12
=1+1-1/2+1/2-1/3+1/3-1/4+……+1/11-1/12
=2-1/12
=23/12

1+1/2+1/6+1/12+20/1+30/1+42/1+56/1+...+1/132
=1+1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+1/6-1/7+1/7-1/8+……+1/11-1/12
=2-1/12
=1又11/12

不知道

1/2=1-2/1 1/6=1/2-1/3 1/12=1/3-1/4 ……
所以原式=1+1-1/12=23/12

你中间的20/1,30/1，是不是写错了？