Prove: $ \lim_{n\rightarrow\infty} x ^ {\left(\frac 1 n\right)} = 1 $
126374
Limit of $2^{1/n}$ as $n\to\infty$ is 1
26226
Proving $\lim \limits_{n\to +\infty } \left(1+\frac{x}{n}\right)^n=\text{e}^x$.
54513
Prove $\frac 1{x+1}<\ln\left(\frac{x+1}x\right)<0.5\left(\frac 1x+\frac 1{x+1}\right)$
45806
Finding $\lim\limits_{n \rightarrow \infty}\left(\int_0^1(f(x))^n\,\mathrm dx\right)^\frac{1}{n}$ for continuous $f:[0,1]\to[0,\infty)$
75268
Proving that $\lim_{n\rightarrow \infty} \frac{n^k}{2^n}=0$
31836
Proof of $\lim_{n\to \infty} \sqrt[n]{n}=1$
7309
Why $\lim\limits_{n\to \infty}\left(1+\frac{1}{n}\right)^n$ doesn't evaluate to 1?
132948
Prove if $\left\{x_n\right\}$ converges to $2$, then $\left\{\frac{1}{x_n}\right\}$ converges to $\frac{1}{2}$
154506
Evaluating $\lim_{n\rightarrow\infty} (\frac{(1+\frac{1}{n})^n}{e})^n$
47606
Proving $\lim_{n\to\infty} a^{\frac{1}{n}}=1$ by definition of limit
27717
Compute $\lim_{x\to\infty}x\;\left[\left(1+\frac{1}{x}\right)^x-e\right]$
135731
Is there a way to show that $e^x=\lim_{n\to \infty }\left(1+\frac{x}{n}\right)^n$?
59339
How to prove that $ \lim_{n\to\infty}\left( \sum_{r=1}^n \dfrac 1 {\sqrt{n^2 + r}} \right) = 1$
111418
Finding lim${_{n \rightarrow \infty}}\left( \frac{n^3}{2^n} \right)$
34127
Prove $\lim_{x \rightarrow 0} \frac {\sin(x)}{x} = 1$ with the epsilon-delta definition of limit.
143227
Show that: $\lim \limits_{n\to\infty}\frac{x_n-x_{n-1}}{n}=0 $
66441
Prove that $|x|<1$ implies that $\lim_{n \to \infty} x^n=0$