Value of the sum, $\sum_{n=1}^{\infty}\left(\frac{\sin(n)}{n}\right)$
43368
How to prove $\sum\limits_{n=1}^\infty\frac{\sin(n)}n=\frac{\pi-1}2$ using only real numbers.
26541
Is $\sum_{n=1}^{\infty}{\frac{\sin(nx)}n}$ continuous?
134576
Does this series converge or diverge? $\sum_{n=1}^\infty\ln\left(1+\frac1{n^2}\right)$
21855
Prove $\sum_{n=1}^{\infty}\arctan{\left(\frac{1}{n^2+1}\right)}=\arctan{\left(\tan\left(\pi\sqrt{\frac{\sqrt{2}-1}{2}}\right)\cdots\right)}$
43903
Find the sum for $\sum_{n=1}^{\infty}(-1)^{(n+1)}\frac{2n+1}{3^n} $
131023
Evaluate the sum: $\sum\limits_{n=0}^{\infty} \frac1{F_{(2^n)}}$
8733
Leibniz test $\sum\limits_{n=1}^\infty \sin\left(\pi \sqrt{n^2+\alpha}\right)$
7881
For what values of $a$ does $\sum_{n=1}^\infty \left( 1+\frac12 + \dotsb + \frac1n \right) \frac{\sin (na)}{n}$ converge?
22636
Find the sum of the series $\sum \limits_{n=1}^{\infty} \frac{2^{-n}(n+3)}{(n+1)(n+2)}$
72568
Calculation of $\lim_{n\to \infty}\prod_{r=1}^{n} \left(1+\frac{r}{n}\right)^{\frac{1}{n}}$
47706
Find the value of $ \sum_{n=1}^{\infty} \frac{n^3}{3^n} $
64223
Infinite Series $\sum\limits_{n=1}^\infty\left(\frac{H_n}n\right)^2$
150928
Summation of a trigonometric series - $\frac{\sin n}{n}$
162
Determine the convergence of $ \sum_{n=1}^{\infty}\left[1-\cos\left(1 \over n\right)\right] $
91784
Calculating $\sum_{n=1}^\infty {\frac{1}{2^nn(3n-1)}}$
9124
Find the exact value of the infinite sum $\sum_{n=1}^\infty \big\{\mathrm{e}-\big(1+\frac1n\big)^{n}\big\}$
125813
Convergence of $ \sum_{n=1}^\infty\left(\exp(\frac{(-1)^n}{n})-1\right)$?