求limn^2(k/n-1/n+1-1/n+2-…-1/n+k)(其中k为与n无关的正整数)n趋向无穷
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求limn^2(k/n-1/n+1-1/n+2-…-1/n+k)(其中k为与n无关的正整数)n趋向无穷
求limn^2(k/n-1/n+1-1/n+2-…-1/n+k)(其中k为与n无关的正整数)n趋向无穷
求limn^2(k/n-1/n+1-1/n+2-…-1/n+k)(其中k为与n无关的正整数)n趋向无穷
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*[(1/n(n+1))+(2/n(n+2))+……+(k/n(n+k))]
=lim (n^2/n(n+1))+(2n^2/n(n+2))+……+(kn^2/n(n+k))
因为k为有限数,故
=lim (n^2/n(n+1)) + lim (2n^2/n(n+2)) + …… + lim (kn^2/n(n+k))
=1+2+……+k
=(1+k)*k/2
有不懂欢迎追问
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