What values of alpha guarantee the convergence of $\sum _{n=0}^{\infty }\left( \frac {\alpha n} {n+1}\right) ^{n}$?
9662
For what real values of $a$ does $\sum_{n=1}^{\infty}{(\frac{an}{n +1})^n}$ converge?
142509
If $\alpha\in (0,1]$ and $x_n=\alpha x_{n-1}+(1-\alpha)x_{n-2}$, show that the sequence $\{x_n\}$ is convergent.
141200
How do I check the series $\sum_{n=2}^{\infty} \frac{(-1)^n }{n+(-1)^n}$ for absolute convergence/conditional convergence?
105980
On convergence of Bertrand series $\sum\limits_{n=2}^{\infty} \frac{1}{n^{\alpha}\ln^{\beta}(n)}$ where $\alpha, \beta \in \mathbb{R}$
35439
Does the series $\;\sum\limits_{n=0}^{\infty}\left(\frac{\pi}{2} - \arctan(n)\right)$ converge or diverge?
121617
Closed form of $\sum_{n=0}^{\infty} \frac{\cos(\alpha \, n)}{n!}$
38062
Proving the convergence of $\sum\limits_{n=1}^{\infty}\frac{1}{1+z^n}$ for $|z| > 1$
62321
To test the convergence $\sum{\frac{1}{(\ln {n})^{\ln{n}}}}$
131518
Test for convergence $\sum_{n=1}^{\infty}\{(n^3+1)^{1/3} - n\}$
25503
Convergence of $\sum_{n=1}^\infty \frac{\sin^2(n)}{n}$
158741
Convergence of $\sum \frac{a_n}{(a_1+\ldots+a_n)^2}$
1098
Does $\sum\limits_{n=1}^\infty\frac{1}{\sqrt{n}+\sqrt{n+1}}$ converge?
35885
Monotonicity and convergence of the sequence $a_n=\sum_{k=1}^{n}\frac{1}{k+n}$
63612
Determine convergence of $\sum_{n=1}^{\infty}a_n$
14050
Determining precisely where $\sum_{n=1}^\infty\frac{z^n}{n}$ converges?
35435
For what values of $\alpha$, does this integral converge?
27323
Convergence of the complex series $\sum_{n=0}^{\infty} \frac{(-1)^{n}}{z+n}$