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

题目

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

答案

1+1/2+1/6+1/12+.+1/132
=1+(1-1/2)+(1/2-1/3)+(1/3-1/4)+.+(1/11-1/12)
=1+1-1/2+1/2-1/3+1/3-1/4+.+1/11-1/12
=2-1/12
=1又11/12