计算1/2-1/6-1/12-1/20-1/30-1/42…-1/132.

题目

计算1/2-1/6-1/12-1/20-1/30-1/42…-1/132.
提示：1/2=1-1/2,1/6=1/2-1/3,1/12=1/3-1/4,…
练习上是这么写的,

答案

可化为
1/(1x2)-1/(2x3)-1/(3x4)...-1/(11x12)
=1/2-(1/2-1/3)-(1/3-1/4)-...-(1/11-1/12)
=1/2-1/2+1/3-1/3+1/4-...-1/11+1/12
=1/12