Prove $\lim_{n \to \infty}$ $(1+\frac xn-o(\frac 1n))^n=e^x$
75791
What is the proper way to handle the limit with little-$o$?
71743
$\lim (1+\frac{1}{n+1})^n = e$
38062
Proving the convergence of $\sum\limits_{n=1}^{\infty}\frac{1}{1+z^n}$ for $|z| > 1$
117370
$\lim_{n\to\infty} \left(1+\frac{2}{n}\right)^{n^2} e^{-2n}$
54775
Find $\lim_{n \to \infty} n[(1+\frac{1}{n})^n - e]$
97571
Find the limit $ \lim_{n\to \infty} 2^{\frac{1}{n}}$
2449
Prove that $\lim \limits_{n \to \infty} \frac{x^n}{n!} = 0$, $x \in \Bbb R$.
74170
Prove that $\lim_{x \to +\infty} \frac{f(x)}{x} = L$ if $\lim_{x \to +\infty} [f(x+1) - f(x)] = L \space$
135731
Is there a way to show that $e^x=\lim_{n\to \infty }\left(1+\frac{x}{n}\right)^n$?
36384
Q: $\lim_{n\to \infty}\left(1 + \frac{1}{n}\right)^{n} = e$
31836
Proof of $\lim_{n\to \infty} \sqrt[n]{n}=1$
91901
Prove that $\lim_{n\to\infty}a_n\le \lim_{n\to\infty}b_n$
44668
Limit of $x\left(\left(1 + \frac{1}{x}\right)^x - e\right)$ when $x\to\infty$
114924
What is $ \lim_{n\to\infty}\frac{1}{e^n}\Bigl(1+\frac1n\Bigr)^{n^2}$?
5436
How to prove $\lim \limits_{x \to 1^-} \sum\limits_{n=0}^\infty (-1)^nx^{n²} = \frac{1}{2} \ $?
99752
how does one solve $\lim_{n\to \infty} (\frac{n^{2}-2n+1}{n^{2}-4n+2})^{n}$
93408
Trying to show that $\ln(x) = \lim_{n\to\infty} n(x^{1/n} -1)$