Why do we have $\lim \sqrt {2 - \sqrt {2 + \sqrt {2 + \sqrt 2 ...}}} (1/2)^n = \pi $?
48086
Why is this series of square root of twos equal $\pi$?
146663
Limit $\lim_{n \to \infty} \frac {a_n}{2^{n-1}}=\frac 4{\pi}$ for $a_{n+1}=a_n+\sqrt{1+a_n^2}$ and $a_0=0$
143207
What is $\sum\limits_{i=1}^n \sqrt i\ $?
17289
prove $\sqrt{a_n b_n}$ and $\frac{1}{2}(a_n+b_n)$ have same limit
125538
limit of $n^{\frac{1}{\sqrt{n}}}$
14013
How to prove that $\lim \frac{1}{n} \sqrt[n]{(n+1)(n+2)... 2n} = \frac{4}{e}$
88425
Prove that $\,\sqrt [n] n < 1 + \sqrt{\frac{2}{n}}\,$
126484
Why is $\Gamma\left(\frac{1}{2}\right)=\sqrt{\pi}$?
47895
Prove $\lim\limits_{n\to\infty}n^{-1/(p+1)}(1^{1^p}\cdot 2^{2^p}\cdots n^{n^p})^{n^{-p-1}}=e^{-1/(p+1)^2}$
28461
Show that $\lim_{n\to\infty} \sum_{k=1}^{n} \frac{n}{n^2+k^2}=\frac{\pi}{4}$
47325
Limit of quotients with square roots: $\lim_{x\to2} \frac{\sqrt{6-x}-2}{\sqrt{3-x}-1}$
64001
What is the result of $\lim\limits_{x \to 0}(1/x - 1/\sin x)$?
52331
What is $\lim_{n\to \infty }\left(\sqrt[\leftroot{-2}\uproot{2}n+1]{(n+1)!}-\sqrt[\leftroot{-2}\uproot{2}n]{n!}\right)$?
83290
How is the value of $\pi$ ( Pi ) actually calculated?
151593
Prove that the limit of $\sqrt{n+1}-\sqrt{n}$ is zero
26783
If $(1+\sqrt{2})^n=a_{n}+b_{n}\sqrt{2}\;,(\forall n\in \mathbb{N}).$Then $\lim_{n\rightarrow \infty}\frac{a_{n}}{b_{n}} = $
52943
How to show $\lim_{\epsilon \rightarrow 0} \frac{\epsilon}{x^2+\epsilon ^2} = \pi \delta (x)$?