Proving $\lim_{n\to\infty} n\left(\left(1+\frac{1}{n}\right)^{n}-e\right)=-\frac{e}{2}$
44668
Limit of $x\left(\left(1 + \frac{1}{x}\right)^x - e\right)$ when $x\to\infty$
18353
Evaluate of $\lim_{n\rightarrow \infty}\left(\frac{n+1}{n}\right)^{n^2}\cdot \frac{1}{e^n}$
5072
To evaluate limit of sequence $\left(\left( 1 + \frac1n \right) \left( 1 + \frac2n \right)\cdots\left( 1 + \frac nn \right) \right)^{1/n}$
76756
A convergence proof: $\lim_{n\to\infty} \left(1+n^2\right)^{\frac1n}$
98365
How to evaluate $\lim_{x \rightarrow \infty} \left(\left(\frac{x+1}{x-1}\right)^x -e^2\right){x}^2$
49102
Evaluating $\lim_{n \to \infty}\left({^n\mathrm{C}_0}{^n\mathrm{C}_1}\dots{^n\mathrm{C}_n}\right)^{\frac{1}{n(n+1)}}$
94910
How does one show that $\lim_{x\rightarrow\infty}\left(1+\frac{1}{x}\right)^x$ converges?
104853
Proving that $\lim\limits_{n\to\infty}n\left( \int_0^1 f(t)\, dt -\frac1n\sum_{k=0}^{n-1}f\left(\frac k n\right) \right)=\frac{f(1)-f(0)}{2}$
143227
Show that: $\lim \limits_{n\to\infty}\frac{x_n-x_{n-1}}{n}=0 $
49128
How to prove $\lim\limits_{n \to \infty} (1+\frac1n)^n = e$?
35169
Finding the limit of $\left(\frac{n}{n+1}\right)^n$
50398
Limit $\lim\limits_{n\to\infty}\left(\frac{n}{n^2+1}+\frac{n}{n^2+2}+\frac{n}{n^2+3}+\cdots+\frac{n}{n^2+n}\right)$
44095
Prove that $\lim_{x\to \infty}\left(x-\ln\cosh x\right)=\ln 2$
71743
$\lim (1+\frac{1}{n+1})^n = e$
98367
Limit of $\left(\frac{n^2+2}{2n^2+1}\right)^{n^2}$
57203
Prove that $\lim_{x \to \infty}\big(\frac{x}{x-1}\big)^x$ is also $e$.
156141
Limit of $\left(1-\frac{1}{n^2}\right)^n$