Why is $\lim_{x\to 1}\sqrt{1-x}\sum_{n=0}^\infty x^{n^2}=\sqrt{\pi}/2\,\,$?
47575
Compute the limit of $\sqrt{1-a}\sum\limits_{n=0}^{+\infty} a^{n^2}$ when $a\to1^-$
147165
Does the fact that $\sum_{n=1}^\infty 1/2^n$ converges to $1$ mean that it equals $1$?
112772
Is the series $\sum \limits_{n=1}^{\infty} \sin(n^2)$ convergent?
125538
limit of $n^{\frac{1}{\sqrt{n}}}$
128181
Find $\lim_{n\to\infty}{\sqrt{n+1}-\sqrt{n}}$ with basic methods
125860
Showing that $\lim\limits_{n\to\infty}x_n$ exists, where $x_{n} = \sqrt{1 + \sqrt{2 + \sqrt{3 + ...+\sqrt{n}}}}$
33965
Convergence of $\sum_{n=1}^\infty (-1)^n(\sqrt{n+1}-\sqrt n)$
48985
Calculating $\lim_{x\to+\infty}(\sqrt{x^2-3x}-x)$
47895
Prove $\lim\limits_{n\to\infty}n^{-1/(p+1)}(1^{1^p}\cdot 2^{2^p}\cdots n^{n^p})^{n^{-p-1}}=e^{-1/(p+1)^2}$
67271
$\sum_{n=-\infty}^{\infty}\frac{1}{(u +n)^2}=\frac{\pi^2}{(\sin \pi u)^2}$
104878
What is the limit $\lim\limits_{n \to \infty} \frac{n^{\sqrt{n}}}{2^n}$?
17534
Find $\lim_{n\to \infty}({1\over \sqrt{n^2+1}}+{1\over \sqrt{n^2+2}}+\cdots+{1\over \sqrt{n^2+n}})$
52331
What is $\lim_{n\to \infty }\left(\sqrt[\leftroot{-2}\uproot{2}n+1]{(n+1)!}-\sqrt[\leftroot{-2}\uproot{2}n]{n!}\right)$?
147930
Does $\sum_{n=1}^{\infty}\frac {\sin{\frac 1 n}} {\sqrt n}$ converge?
146528
Define $I_n=\int_0^1\frac{x^n}{\sqrt{x^2+1}}dx$ for every $n\in\mathbb{N}$. Prove that $\lim_{n\to\infty}nI_n=\frac{1}{\sqrt 2}$.
148320
Find the limit $\lim_\limits{n\to{\infty}}n^2(\sqrt[n]{x}-\sqrt[{n + 1}]{x})$ and my inquiry about Stolz-Cesàro theorem
136602
Why is $\int_1^{\infty}(1/x^2)\,dx$  less than $\sum_{n=1}^{\infty} 1/(n^2)$?