Limit of $f_{n+1} = \sqrt{12 + f_n}$ with proof by contradiction
686
$\sqrt{c+\sqrt{c+\sqrt{c+\cdots}}}$, or the limit of the sequence $x_{n+1} = \sqrt{c+x_n}$
925
Prove that $F_n={n-1 \choose 0 }+{n-2 \choose 1 }+{n-3 \choose 2 }+\ldots$ where $F(n)$ is the $n$-th fibonacci number
34308
Given $|z|<1$ prove $\lim_{n \to \infty} z^n=0$.
50673
Limit of ${a_n}^{1/n}$ is equal to $\lim_{n\to\infty} a_{n+1}/a_n$
144310
How would you prove that $\lim\limits_{n\to\infty}(\sqrt{4n^2+n}-2n)=\frac14$?
5728
How to prove $\lim_{n \to \infty} \sqrt{n}(\sqrt[n]{n} - 1) = 0$?
80920
Prove or disprove: For any $v\in\mathbb{R}^n, \|v\|_1\|v\|_\infty \leq \frac{1+\sqrt{n}}{2}\|v\|_2^2$
157539
Prove: $\lim\limits_{n\to\infty}\frac{1}{n}\sum\limits_{k=1}^{n}\sqrt{1+\frac{k}{n}}=\frac{2}{3}(2\sqrt{2}-1)$
105064
What is wrong with this fake proof that $\lim\limits_{n\rightarrow \infty}\sqrt[n]{n!} = 1$?
67084
Prove or disprove that $\lim_{n \to \infty} {n \choose k} / a^n = 0$ for all $k \in \mathbb{Z_+}, a \in \mathbb{R}: a> 1$.
12031
Asymptotic behavior of the sequence $a_n=\sqrt{n+a_{n-1}}$
87116
Prove $ \lim_{n\to \infty}\frac{n}{n+1} = 1$ using Cauchy (epsilon) definition of a limit of a sequence
5797
Limit of the sequence $a_n=\sqrt[n+1]{(n+1)!}-\sqrt[n]{n!}$
33976
Prove that $\lim_{n \to \infty} \sqrt[n]{a} = 1$ using only the basic properties of sequences
59339
How to prove that $ \lim_{n\to\infty}\left( \sum_{r=1}^n \dfrac 1 {\sqrt{n^2 + r}} \right) = 1$
135700
Show that $\lim_{n \to \infty} (1/n)\sum_{i=1}^n f(x_i)$ exists
4024
Finding the limit of $\frac {n}{\sqrt[n]{n!}}$