1/2+1/6+1/12+1/20+1/30+1/42+1/56 (能用简便方法的要用简便算法）要说用什么律

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1/2+1/6+1/12+1/20+1/30+1/42+1/56 (能用简便方法的要用简便算法）要说用什么律
1/2+1/6+1/12+1/20+1/30+1/42+1/56 (能用简便方法的要用简便算法）要说用什么律

1/2+1/6+1/12+1/20+1/30+1/42+1/56 (能用简便方法的要用简便算法）要说用什么律
列项求和
1/n(n+1)=1/n-1/(n+1)
如1/6=1/2*3=1/2-1/3
故1/2+1/6+1/12+1/20+1/30+1/42+1/56
=1/1*2+1/2*3+1/3*4+1/4*5+1/5*6+1/6*7+1/7*8
=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
=1-1/8
=7/8