1/2+1/6+1/12+1/20+1/30+1/42+1/7怎么简算?如题

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1/2+1/6+1/12+1/20+1/30+1/42+1/7怎么简算?如题
1/2+1/6+1/12+1/20+1/30+1/42+1/7怎么简算?如题

1/2+1/6+1/12+1/20+1/30+1/42+1/7怎么简算?如题
1/2+1/6+1/12+1/20+1/30+1/42+1/7 =（1/2+1/6+1/12+1/20+1/30+1/42）+1/7 =1-1/2+1/(2*3)+1/(3*4)+1/(4*5)+1/(5*6)+1/(6*7) +1/7 =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