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lim-x-log-n-n-n-k-1-k-n-k-




Question Number 199012 by universe last updated on 26/Oct/23
  lim_(x→∞)  ((log n)/n)^(  n) (√(Σ_(k=1) ^∞  (k^n /(k!))))   =   ????
$$\:\:\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\frac{\mathrm{log}\:{n}}{{n}}\:^{\:\:{n}} \sqrt{\underset{{k}=\mathrm{1}} {\overset{\infty} {\sum}}\:\frac{{k}^{{n}} }{{k}!}}\:\:\:=\:\:\:???? \\ $$

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