1/2+1/6+1/12+1/20+1/30+1/42+1/56+1/72+1/90+1/110=多少的简便运算

答案是10/11~~~~~~~~~~~~~~~1/[n*(n+1)]=(1/n)-[1/(n+1)]
所以式子是1-1/11=10/11

全部都对。来晚了

1/2+1/6+1/12+1/20+1/30+1/42+1/56+1/72+1/90+1/110
=(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）+（1/8-1/9）+（1/9-1/10）+（1/10-1/11）
=1-1/11=10/11

1/2+1/6+1/12+1/20+1/30+1/42+1/56+1/72+1/90+1/110
=1/(1×2)+1/(2×3)+1/(3×4)+...+1/(10×11)
=1-1/2+1/2-1/3+1/3-1/4+...+1/10-1/11
=1-1/11
=10/11本回答被网友采纳