
1道数列极限题
计算limn^2(k/n-1/(n+1)-1/(n+2)-......-1/(n+k))1楼回答不正确无数个极限为0加起来不等于0...
计算 lim n^2(k/n-1/(n+1)-1/(n+2)-......-1/(n+k))
1楼回答不正确 无数个极限为0加起来不等于0 展开
1楼回答不正确 无数个极限为0加起来不等于0 展开
2个回答
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lim n^2(k/n-1/(n+1)-1/(n+2)-......-1/(n+k))
=lim n^2{[1/n-1/(n+1)]+[1/n-1/(n+2)]......+[1/n-1/(n+k)]
=lim n^2/[n(n+1)]+n^2*2/[n(n+2)]+......+n^2*k/[n(n+k)]
=1+2+......k
=k*(k+1)/2
=lim n^2{[1/n-1/(n+1)]+[1/n-1/(n+2)]......+[1/n-1/(n+k)]
=lim n^2/[n(n+1)]+n^2*2/[n(n+2)]+......+n^2*k/[n(n+k)]
=1+2+......k
=k*(k+1)/2
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