1/2+1/6+1/12+1/20+1/30+1/42+1/56+1/72+1/90+1/110=?用简便运算!

题目

1/2+1/6+1/12+1/20+1/30+1/42+1/56+1/72+1/90+1/110=?用简便运算!
求.

答案

1/2+1/6+1/12+1/20+1/30+1/42+1/56+1/72+1/90+1/110=
=1/2+(1/2-1/3)+(1/3-1/4)+.*(1/9-1/10)+(1/10-1/11)
=1-1/11
=10/11.