Sn=1/1*2+1/2*3+1/3*4+…+1/n*(n+1),n属于正整数.求S10
人气：470 ℃ 时间：2020-05-26 11:07:40
解答
1/[n(n+1)]=(1/n)-[1/(n+1)].如1/(1×2)=1-(1/2).1/(2×3)=(1/2)-(1/3).1/(3×4)=(1/3)-(1/4).1/[n(n+1)]=(1/n)-[1/(n+1)].将这些等式累加得：Sn=1/1×2+1/2×3+1/3×4+1/4×5+...+1/n×(n+1)=1-[1/(n+1)].当n=10时,S10=1-(1/11)==10/11.
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