Give an example of a series such that $\sum a_n$ is convergent but $\sum a_{3n}$ is divergent
40437
Example of a series!
143201
$\sum a_n$ and $\sum b_n$ converges. Prove $\sum a_nb_n$ converges.
33419
If $a_n$ is a strictly increasing unbounded sequence, does $\sum_n \frac{a_{n+1} - a_n}{a_n}$ diverge?
113684
Does series with factorials converge/diverge: $\sum\limits_{n=1}^\infty \frac{4^n n!n!}{(2n)!}$?
7198
How can I show whether the series $\sum\limits_{n=1}^\infty \frac{(-1)^n}{n(2+(-1)^n)} $ converges or diverges?
43542
If a $\{a_n\}$ diverges, so $a_n \rightarrow + \infty$, how to find sequence $\{b_n\}$ such that $\sum |b_n|<\infty$ but $\sum |a_n||b_n|$ diverges?
149240
Divergence of a series
123108
Does the series $ \sum\limits_{n=1}^{\infty} \frac{1}{n^{1 + |\sin(n)|}} $ converge or diverge?
90936
how prove $\sum_{n=1}^\infty\frac{a_n}{b_n+a_n} $is convergent?
32637
What is the sum of this series: $\displaystyle\sum_{n=0}^{\infty} \dfrac{a^n}{(3n)!}$
27061
Is $\sum\limits_{n=1}^{\infty}\frac{n!}{n^n}$ convergent?
138884
If series of terms $a_j, b_j$ are convergent, must $\sum_j^\infty a_j b_j$ be convergent?
67303
If $\sum_{n=2}^{\infty} a_n$ is convergent, is $\sum_{n=2}^{\infty}{\sqrt{a_n} \over \ln{n}}\left( n^{a_n}-1 \right)$ convergent as well?
3735
If $\sum_{1}^{\infty}(a_n)^3$ diverges, does $\sum_{1}^{\infty}(a_n)$?
59113
Convergence of product of convergent series
17504
Divergent infinite series $n!e^n/n^n$ - simpler proof of divergence?
158703
Is series $\sum_{n=1}^{\infty}\frac{\cos(nx)}{n^\alpha}$, for $\alpha>0$, convergent?