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Question-155357




Question Number 155357 by mathlove last updated on 29/Sep/21
Commented by mathlove last updated on 30/Sep/21
pleas answer
$${pleas}\:{answer} \\ $$
Answered by qaz last updated on 10/Mar/22
lim_(n→∞) (1+n)^(1/H_n ) =lim_(n→∞) e^((ln(1+n))/(lnn+γ)) =e
$$\underset{\mathrm{n}\rightarrow\infty} {\mathrm{lim}}\left(\mathrm{1}+\mathrm{n}\right)^{\frac{\mathrm{1}}{\mathrm{H}_{\mathrm{n}} }} =\underset{\mathrm{n}\rightarrow\infty} {\mathrm{lim}e}^{\frac{\mathrm{ln}\left(\mathrm{1}+\mathrm{n}\right)}{\mathrm{lnn}+\gamma}} =\mathrm{e} \\ $$

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