Limit of: $\lim\limits_{x\to \infty}\left(\frac{1}{n}\sum_{k=1}^{n} k^{1/x}\right)^{nx}$
53918
whats the proof for $\lim_{x → 0} [(a_1^x + a_2^x + .....+ a_n^x)/n]^{1/x} = (a_1.a_2....a_n)^{1/n}$
104853
Proving that $\lim\limits_{n\to\infty}n\left( \int_0^1 f(t)\, dt -\frac1n\sum_{k=0}^{n-1}f\left(\frac k n\right) \right)=\frac{f(1)-f(0)}{2}$
56265
limit $\lim\limits_{n\to\infty}\left(\sum\limits_{i=1}^{n}\frac{1}{\sqrt{i}} - 2\sqrt{n}\right)$
50334
What is $\lim_{n \rightarrow \infty}\sum\limits_{k = 1}^n\frac{k}{n^2}$?
11489
Limit of $s_n = \int\limits_0^1 \frac{nx^{n-1}}{1+x} dx$ as $n \to \infty$
27717
Compute $\lim_{x\to\infty}x\;\left[\left(1+\frac{1}{x}\right)^x-e\right]$
26226
Proving $\lim \limits_{n\to +\infty } \left(1+\frac{x}{n}\right)^n=\text{e}^x$.
98367
Limit of $\left(\frac{n^2+2}{2n^2+1}\right)^{n^2}$
93095
Find $\lim\limits_{n \to \infty}\left(1-\frac{1}{2^2}\right)\left(1-\frac{1}{3^2}\right)\cdots\left(1-\frac{1}{n^2}\right)$
17872
Evaluate $\lim\limits_{n\to\infty}\frac{\sum_{k=1}^n k^m}{n^{m+1}}$
135731
Is there a way to show that $e^x=\lim_{n\to \infty }\left(1+\frac{x}{n}\right)^n$?
36384
Q: $\lim_{n\to \infty}\left(1 + \frac{1}{n}\right)^{n} = e$
156141
Limit of $\left(1-\frac{1}{n^2}\right)^n$
107386
Compute $\lim_{n \to \infty} \int_0^{\frac{\pi}{2}} \sum_{k=1}^n (\sin{x})^kdx$
54830
Find the limit $\lim\limits_{x\to\infty} f(x)= \lim\limits_{x \to \infty} \left(\frac{x}{x+1}\right)^x$
113336
Limit of $(\frac{1}{n^2})^{(\frac{1}{n})}$
72842
Evaluation of the limit $\lim\limits_{n \to \infty } \frac1{\sqrt n}\left(1 + \frac1{\sqrt 2 }+\frac1{\sqrt 3 }+\cdots+\frac1{\sqrt n } \right)$