1/2+1/2+3+1/2+3+4+1/+2+3+ - 知识问答

1/2+1/2+3+1/2+3+4+1/+2+3+4+1/2+3+4+……200

1个回答

网上搜索的答案,
2+3+4+……+n=(n+2)(n-1)/2
∴1/(2+3+4+……+n)=2/(n+2)(n-1)=(2/3)[(1/n-1)-(1/n+2)]
∴原式=(2/3)(1/1-1/4+1/2-1/5+……+1/199-1/202)
=(2/3)(1+1/2+1/3-1/200-1/201-1/202)
=15008602/12180600

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