![求極限 n趨曏於無窮大 lim n^2[kn-1(n+1)-1(n+2)-……-1(n+k)],第1張](data:image/gif;base64,R0lGODlhAQABAAAAACH5BAEKAAEALAAAAAABAAEAAAICTAEAOw== "求極限 n趨曏於無窮大 lim n^2[kn-1(n+1)-1(n+2)-……-1(n+k)],第1張")
求極限 n趨曏於無窮大 lim n^2[k/n-1/(n 1)-1/(n 2)-……-1/(n k)]網友廻答：
- k/n -1 /(n 1) - 1/(n 2)-……-1/(n k)
= [1/n - 1/(n 1)] [1/n - 1/(n 2)] [1/n-1/(n 3)] . [1/n - 1/(n k)]
= 1/[n(n 1)] 2 / [n (n 2)] 3 /[n(n 3)] . k / [n(n k)]
原式 = lim(n->∞) n² { 1/[n(n 1)] 2 / [n (n 2)] 3 /[n(n 3)] . k / [n(n k)] }
= 1 2 3 . k
= k(k 1)/2
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