How to show that $\exists \lim_{x\rightarrow1^{-}}\sum_{n=0}^{+\infty} (-1)^n x^{n^2} = 1/2$?
5436
How to prove $\lim \limits_{x \to 1^-} \sum\limits_{n=0}^\infty (-1)^nx^{n²} = \frac{1}{2} \ $?
569
How do I determine $\lim_{x\to\infty} \left[x - x^{2} \log\left(1 + 1/x\right)\right]$?
64223
Infinite Series $\sum\limits_{n=1}^\infty\left(\frac{H_n}n\right)^2$
75268
Proving that $\lim_{n\rightarrow \infty} \frac{n^k}{2^n}=0$
72693
Prove: $\lim_{x\to\infty}x^{2/3}((x+1)^{1/3}-x^{1/3})=1/3$
62443
Prove that $\sum_{n=1}^\infty \ln\left(\frac{n(n+2)}{(n+1)^2}\right)$ converges and find its sum
52943
How to show $\lim_{\epsilon \rightarrow 0} \frac{\epsilon}{x^2+\epsilon ^2} = \pi \delta (x)$?
14129
How to prove that $\lim \limits_{n\rightarrow \infty} \frac{F_{n+1}}{F_n}=\frac{\sqrt{5}+1}{2}$
71240
The limit of a sum $\sum_{k=1}^n \frac{n}{n^2+k^2}$ as $n\rightarrow\infty$
94910
How does one show that $\lim_{x\rightarrow\infty}\left(1+\frac{1}{x}\right)^x$ converges?
54893
$ \lim\limits_{x \rightarrow \ + \infty}(\sqrt{x^2 + 2x} - \sqrt{x^2 - 7x})$
8387
Evaluate $\lim_{n \rightarrow \infty} \frac {[(n+1)(n+2)\cdots(n+n)]^{1/n}}{n}$
56265
limit $\lim\limits_{n\to\infty}\left(\sum\limits_{i=1}^{n}\frac{1}{\sqrt{i}} - 2\sqrt{n}\right)$
144403
Limit $\lim_{x\rightarrow +\infty}\sqrt{x}e^{-x}\left(\sum_{k=1}^{\infty}\frac{x^{k}}{k!\sqrt{k}}\right)$
17332
How to compute $\sum\limits_{n=1}^{\infty}\frac{1}{x^n-1}$?
33965
Convergence of $\sum_{n=1}^\infty (-1)^n(\sqrt{n+1}-\sqrt n)$
156557
How to compute $\lim_{n\rightarrow\infty}e^{-n}\left(1+n+\frac{n^2}{2!}\cdots+\frac{n^n}{n!}\right)$