1/3+1/6+1/10+1/15+1/21+…1 - 知识问答

1/3+1/6+1/10+1/15+1/21+…1/55

3个回答

1/3+1/6+1/10+1/15+1/21+…1/55
=2*(1/6+1/12+1/20+1/30+1/42+…1/110)
=2*[(1/2-1/3)+(1/3-1/4)+(1/4-1/5)+(1/5-1/6)+(1/6-1/7)+.+(1/10-1/11)]
=2*[1/2-1/11]
=1-2/11
=9/11

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