I can't get a result for $\sum\limits_{k=0}^\infty \frac1{k^2+1}$.
28378
Find the infinite sum of the series $\sum_{n=1}^\infty \frac{1}{n^2 +1}$
97720
Asymptotic behavior of $\sum\limits_{k=1}^n \frac{1}{k^{\alpha}}$ for $\alpha > \frac{1}{2}$
136444
Evaluating $\sum_{n=0}^\infty\frac{(-1)^n}{3n+1}$
50435
Infinite Series $‎\sum\limits_{n=2}^{\infty}\frac{\zeta(n)}{k^n}$
89698
Please help with $\sum\limits_{r=1}^{N}\frac{2r+3}{3^r(r+1)}$
16143
How can I prove that $\sum_{n=1}^\infty \frac{1}{n(n+1)} = 1$?
99420
Compute $\sum_{n=1}^\infty \frac{1}{(n+1)\sqrt[]{n}+n\sqrt[]{n+1}}$
110568
Does $\sum_{k=1}^{\infty}\ln(\frac{k}{k+1})$ converge/diverges??
90030
What would be the value of $\sum\limits_{n=0}^\infty \frac{1}{an^2+bn+c}$
60104
Evaluate $\sum_{k=1}^\infty\frac{x^k}{k(k+1)}$
158960
How to find limit of the sequence $\sum\limits_{k=1}^n\frac{1}{\sqrt {n^2 +kn}}$?
101052
Find the infinite sum $\sum_{k=1}^{\infty}\sqrt k - 2\sqrt {k + 1} + \sqrt {k + 2} $
149360
convergence of $ \sum_{k=1}^\infty \sin^2(\frac 1 k)$
50812
Partial sum of the series $\sum\limits_{r=1}^{\infty} \frac{1}{r(r+1)}$
50606
Find $\sum\limits_{k\, \text{ odd}} \frac{2(k^2-1)}{k^4+k^2+1}$
111788
Does the series $\sum\limits_{n=1}^\infty \frac{1}{n\sqrt[n]{n}}$ converge?
146651
Evaluting sum $\sum \limits_{n=0}^\infty\frac{n^k}{n!}$