Does the series $\sum \sin{(\sin{(...\sin{(1)}...)})}$ converge?
139113
Does the series $\sum \sin^{(n)}(1)$ converge, where $\sin^{(n)}$ denotes the $n$-fold composition of $\sin$?
65993
Does $\sum_{k=1}^\infty\frac1{k^n}$ converge for $\Re(n)=1,\Im(n)\ne0$?
17028
How to test if $\sum_{n=1}^{\infty }\frac{1}{n^{1+\frac{1}{n}}}$ converges?
6345
Is the $\sum\sin(n)/n$ convergent or divergent?
102581
Does $\sum_{n=1}^{\infty} \frac{1}{n^{1 + 1/n}}$ converge?
41751
$\sum_{n=1}^\infty \frac{i^n}{n}$ converge?
5817
Does the series $\sum \limits_{n=2}^{\infty }\frac{n^{\log n}}{(\log n)^{n}}$ converge?
6908
Convergence/Divergence of some series
21606
Can all real numbers be represented by the sum of a convergent series?
35929
Convergence of series $\sum_{n=1}^{\infty}{\frac{1}{\sqrt{1}+\sqrt{2}+...+\sqrt{n}}}$
126264
Does the series $\sum \limits _{n=0}^{\infty} \cos(n\pi)$ converge or diverge?
98247
Is $ \sum\limits_{n=1}^\infty \frac{|\sin n|^n}n$ convergent？
112823
Convergence of the series $\sum_{1}^\infty \left(1-n\sin(\frac{1}{n})\right)$
69588
Convergence of a given series
128260
If $\sum a_n$ converges, so does $\sum a_n^{\frac{n}{n+1}}$
111464
Does this series (of a form similar to a telescoping series) converge?
109718
Does $\sum \limits_{n=1}^\infty\frac{\sin n}{n}(1+\frac{1}{2}+\cdots+\frac{1}{n})$ converge (absolutely)?