Find the limit of $2^n/x_n$ if $x_1=1$ and $ x_{n+1} = x_{n} + \sqrt{x_n^2 + 1}$ for every $n$
55464
Convergence of sequence given by $x_1=1$ and $x_{n+1}=x_n+\sqrt{x_n^2+1}$
104602
asymptotic of $x^{x^x} = n$
53688
How can one prove that $\lim_{n \to \infty}a^{1/n}=1$ for every $a>0$?
7868
Computing limit of $(1+1/n)^{n^2}$
86205
Evaluating the limit of a sequence given by recurrence relation $a_1=\sqrt2$, $a_{n+1}=\sqrt{2+a_n}$. Is my solution correct?
110749
Determine $\lim\limits_{n \to \infty}{{n} \choose {\frac{n}{2}}}\frac{1}{2^n}$, where each $n$ is even
155353
Find the limit of $ a_n =\left(1+\frac{1^2}{n^2}\right)^1\left(1+\frac{2^2}{n^2}\right)^2\cdots \left(1+\frac{n^2}{n^2}\right)^n$
16634
How to show $\lim_{n \to \infty} \sqrt[n]{a^n+b^n}=\max \{a,b\}$?
123970
Find $L=\lim \limits_{n\to \infty}\sqrt[n]{x^n+y^n+z^n}$
47575
Compute the limit of $\sqrt{1-a}\sum\limits_{n=0}^{+\infty} a^{n^2}$ when $a\to1^-$
107764
Limit series $(a^n-b^n)^{1/n}$
42251
Limit of non-negative real root of $x^n+x^{n-1}+x-1=0$ as $n \to \infty$
20773
Find $\lim\limits_{n \to \infty} \frac{\sqrt 1 + \sqrt 2 + \dots + \sqrt{n}}{n\sqrt{n}}$.
155382
Find $ \lim\limits_{{n \to \infty}} \frac1{2^n} \sum\limits_{k=1}^n \frac1{\sqrt{k}} \binom nk$
9610
Find the sum of $\sum\limits_{n=1}^{\infty} \frac{x^{n}}{n(n+1)}$
33495
A limit problem about $a_{n+1}=a_n+\frac{n}{a_n}$
151593
Prove that the limit of $\sqrt{n+1}-\sqrt{n}$ is zero