Evaluating $\lim\limits_{n\to\infty}(a_1^n+\dots+a_k^n)^{1\over n}$ where $a_1 \ge \cdots\ge a_k \ge 0$
10383
The $ l^{\infty} $-norm is equal to the limit of the $ l^{p} $-norms.
8773
Finding $\lim\limits_{n \to \infty}{\frac{1^1+2^2+3^3+\cdots+n^n}{n^n}}$
15822
Value of $\lim_{n\to \infty}\frac{1^n+2^n+\cdots+(n-1)^n}{n^n}$
102523
Show that $\lim\limits_{n \to \infty} \sup\limits_{k \geq n} \left(\frac{1+a_{k+1}}{a_k}\right)^k \ge e$ for any positive sequence $\{a_n\}$
152557
Calculate $ \lim\limits_{n \to \infty} \sum\limits_{k=0}^n \frac{2^{k-1}}{a^{2k-1}+1} $
108917
Use $\delta-\epsilon$ to show that $\lim_{n\to\infty} a^{\frac{1}{n}} = 1$?
29609
Limits involving factorials $\lim_{N\to\infty} \frac{N!}{(N-k)!N^{k}}$
128181
Find $\lim_{n\to\infty}{\sqrt{n+1}-\sqrt{n}}$ with basic methods
131927
lim inf $|a_n|=0 \implies \sum_{k=1}^\infty a_{n_k}$ converges
17872
Evaluate $\lim\limits_{n\to\infty}\frac{\sum_{k=1}^n k^m}{n^{m+1}}$
47895
Prove $\lim\limits_{n\to\infty}n^{-1/(p+1)}(1^{1^p}\cdot 2^{2^p}\cdots n^{n^p})^{n^{-p-1}}=e^{-1/(p+1)^2}$
437
Show that $\lim_{n\to\infty} \sqrt[n]{a^{n} + b^{n}} = \max(a, b)$
67645
Prove that $\displaystyle{\lim_{n \to \infty}a_n ^{1/k}}= a^{1/k}$ if $a_n \ge 0$ for all $n$ and $\displaystyle{\lim_{n \to \infty}a_n}= a$
9541
Evaluate $\lim_{n\to\infty}\frac {qn+1}{qn} \frac {qn+p+1}{qn+p} \cdots \frac {qn+np+1}{qn+np}$ where $p\in\mathbb{N}\setminus\{0,1\},q>0.$
20843
Evaluate the limit of $\lim_{n\to\infty}\frac{1}{n^2}\left(\frac{2}{1}+\frac{9}{2}+\frac{64}{9}+\cdots+\frac{(n+1)^{n}}{n^{n-1}}\right)$
19100
Find $\lim \limits_{n \to \infty}{1*4*7*\dots(3n+1) \over 2*5*8* \dots (3n+2)}$
122800
Let $a > 0$ and let $k \in \mathbb{N}$. Evaluate the limit