Problem dealing with $\sum \frac{\sin(n)}{n}$ and its convergence
83040
Proving that the sequence $F_{n}(x)=\sum\limits_{k=1}^{n} \frac{\sin{kx}}{k}$ is boundedly convergent on $\mathbb{R}$
150928
Summation of a trigonometric series - $\frac{\sin n}{n}$
125341
Does $\sum_{n=1}^{\infty} \frac{1}{n+1}$ converge?
16642
Showing $a_n=\sin(n)$ does not converge
40079
Convergence of the series $\sum_n \frac{n^{\log(n)}}{\log(n)^n}$
63612
Determine convergence of $\sum_{n=1}^{\infty}a_n$
9244
Does the sequence $\{\sin^n(n)\}$ converge?
2584
Convergence of an alternating series : $ \sum_{n\geq 1} \frac{(-1)^n|\sin n|}{n}$
98247
Is $ \sum\limits_{n=1}^\infty \frac{|\sin n|^n}n$ convergent？
111788
Does the series $\sum\limits_{n=1}^\infty \frac{1}{n\sqrt[n]{n}}$ converge?
119147
How to prove that $\sum_{n=1}^{\infty}\frac{|\sin{(n\theta_0)}|}{n}$ diverges for given $\theta_0\in (0,\pi)$?
40698
Does the series $\sum\limits_{n=1}^\infty \frac{1}{n^3 \sin^2n}$ converge or diverge?
117583
Why does $\sum_{n=0}^\infty (\sin{\frac{1}{n}})(\sinh{\frac{1}{n}})(\cos n)$ converge
143753
Please help me to find the sum $\sum\limits_{n\geq1} \frac{\sin(nx)}{n^2}$
21970
Convergence of the Power Series for $xu''+\sin(x)u=0$
47572
Evaluate $ \sum_{n=1}^{\infty} \frac{\sin \ n}{ n } $ using the fourier series
95353
Does $\sum_{n=1}^\infty \frac{\cos{(\sqrt{n})}}{n}$ converge?