Convergence of the series $\sum_{k=1}^{\infty} \left( \frac{1+\cos k}{2+\cos k}\right)^{2k}$. Check my work.
74903
Find out whether $\sum_{k=1}^{\infty}\left(\frac{1+\cos k}{2+\cos k}\right)^{2k}$ converges absolutely, conditionally or diverges.
50435
Infinite Series $‎\sum\limits_{n=2}^{\infty}\frac{\zeta(n)}{k^n}$
7041
Test for convergence of the series $\sum_{n=2}^\infty\frac{1}{(\ln n)^{\ln n}}$
144078
What does $\sum_{k=0}^\infty \frac{k}{2^k}$ converge to?
7198
How can I show whether the series $\sum\limits_{n=1}^\infty \frac{(-1)^n}{n(2+(-1)^n)} $ converges or diverges?
142985
Finding sum of series $\sum^{\infty}_{k=0}\frac{(k+1)(k+2)}{2^k}$
76867
Does $\sum _{k=2} ^\infty \frac{(-1)^k}{\sqrt{k}+(-1)^k}$ converge conditionally?
25852
Does the series $\sum_{n=1}^\infty$ ${\sqrt{n+1}-\sqrt{n}}\over n$ converge or diverge?
41751
$\sum_{n=1}^\infty \frac{i^n}{n}$ converge?
126264
Does the series $\sum \limits _{n=0}^{\infty} \cos(n\pi)$ converge or diverge?
42742
Is $\sum_{n=1}^\infty \frac{\sin(2n)}{1+\cos^4(n)}$ convergent?
134576
Does this series converge or diverge? $\sum_{n=1}^\infty\ln\left(1+\frac1{n^2}\right)$
57372
Series convergence of $\sum_{n=1}^{\infty}\frac{1}{n^3}$
33965
Convergence of $\sum_{n=1}^\infty (-1)^n(\sqrt{n+1}-\sqrt n)$
49860
Determine the convergence of $\sum\limits_{n=2}^\infty \frac{\sqrt{n+1}}{n(n-1)}$
109718
Does $\sum \limits_{n=1}^\infty\frac{\sin n}{n}(1+\frac{1}{2}+\cdots+\frac{1}{n})$ converge (absolutely)?
68404
Check whether $\sum _{m=1}^{\infty }\sum _{n=1}^{\infty }\frac{1}{\left(m+n\right)^2}$ converges or NOT?