How to show that $\sum_{n=1}^\infty r^n\cos n\theta=\frac{r\cos\theta-r^2}{1-2r\cos\theta+r^2}$?
72377
Show that $\sum_{n=1}^\infty r^n\cos(n\theta)=\dfrac{r\cos\theta -r^2}{1-2r\cos\theta+r^2}$ whenever $0<r<1$.
52987
$\sum_{n=-\infty}^{\infty}\frac{1}{(n+\alpha)^2}=\frac{\pi^2}{(\sin \pi \alpha)^2}$?
92810
What is $\sum_{r=1}^\infty\frac{r+2}{2^{r+1}(r)(r+1)}$?
25503
Convergence of $\sum_{n=1}^\infty \frac{\sin^2(n)}{n}$
121617
Closed form of $\sum_{n=0}^{\infty} \frac{\cos(\alpha \, n)}{n!}$
71413
Proving complex series $1 + \cos\theta + \cos2\theta +... + \cos n\theta $
150148
Sum of $\sum^\infty_{n=2} \frac{1}{\ln{(n!)}}$
16143
How can I prove that $\sum_{n=1}^\infty \frac{1}{n(n+1)} = 1$?
151477
computing the series $\sum_{n=1}^\infty \frac{1}{n^2 2^n}$
7686
How to prove $\sum_{n=0}^{\infty} \frac{n^2}{2^n} = 6$?
117200
Evaluation of $ \sum_{k=0}^n \cos k\theta $
25395
Sum $\sum_{n=1}^\infty \frac{n^2}{(n+2)!}$
99843
How to simplify $ \sum_{k=0}^{\infty} \binom{k + r - 1}{k} x^k$
111524
Information on the sum $\sum_{n=1}^\infty \frac{\log n}{n!}$
127806
How to find the sum of the series $\sum_{k=2}^\infty \frac{1}{k^2-1}$?
117863
Series $\sum_{n=1}^\infty \frac{n^n}{(n!)^2}$
5650
Show $\ln2 = \sum_\limits{n=1}^\infty\frac1{n2^n}$