prove equality $\lim_{n\to\infty}n(\sqrt[n]{a} - 1) = \ln a $
31889
The limit as $n$ approaches infinity of $n(a^{1/n}-1)$
13696
Proving $\limsup\frac 1 {a_n}=\frac 1 {\liminf a_n}$ and $\limsup a_n\cdot \limsup \frac 1 {a_n} \ge 1$
49128
How to prove $\lim\limits_{n \to \infty} (1+\frac1n)^n = e$?
41037
Prove that $f'(a)=\lim_{n\to\infty}\frac{f(b_n)-f(a_n)}{b_n-a_n}$ under some conditions
12976
Prove $\displaystyle\lim_{n\to\infty}\phi(n)=\infty$.
3111
How to prove that if $\lim_{n \rightarrow \infty}a_n=A$, then $\lim_{n \rightarrow \infty}\frac{a_1+...+a_n}{n}=A$
101630
Limit $\lim_{n\to\infty}\sqrt n(\sqrt[n]x-1)$
93408
Trying to show that $\ln(x) = \lim_{n\to\infty} n(x^{1/n} -1)$
25206
How to prove that $\lim\limits_{n\to \infty}a_{n+1}=\lim\limits_{n\to \infty}a_{n}$
64932
Show that $\lim_{x\to a^{+}} g(x) =g(a)$
118138
$\epsilon - \delta$ proof that $\lim_{x \to a} \sqrt x = \sqrt a$
68891
Are the limits $\lim\limits_{n\to \infty }\left|\frac{a_{n+1}}{a_n}\right|\,$ and $\lim\limits_{n\to \infty }\sqrt[n]{|a_n|}\,$ equal?
151593
Prove that the limit of $\sqrt{n+1}-\sqrt{n}$ is zero
17090
Compute $\lim_\limits{n\to\infty}a_n$ where $a_{n+2}=\sqrt{a_n.a_{n+1}}$
437
Show that $\lim_{n\to\infty} \sqrt[n]{a^{n} + b^{n}} = \max(a, b)$
22347
Proving that: $\lim\limits_{n\to\infty} \left(\frac{a^{\frac{1}{n}}+b^{\frac{1}{n}}}{2}\right)^n =\sqrt{ab}$
112388
Suppose $\lim \limits_{n \to ∞} a_n=L$. Prove that $\lim\limits_{n \to ∞} \frac{a_1+a_2+\cdots+a_n}{n}=L$