Give an example of a series $\sum a_n$ such that $\sum a_n$ is convergent but $\sum a_{3n}$ is divergent.
40437
Example of a series!
92031
If $\sum_{n=1}^\infty \frac{1}{a_n}$ converges, must $\sum_{n=1}^\infty \frac{n}{a_1 + \dots + a_n}$ converge?
17201
$y_{2n}, y_{2n+1}$ and $y_{3n}$ all converge. What can we say about the sequence $ y_n$?
7198
How can I show whether the series $\sum\limits_{n=1}^\infty \frac{(-1)^n}{n(2+(-1)^n)} $ converges or diverges?
4672
Example of two convergent series whose product is not convergent.
33419
If $a_n$ is a strictly increasing unbounded sequence, does $\sum_n \frac{a_{n+1} - a_n}{a_n}$ diverge?
40698
Does the series $\sum\limits_{n=1}^\infty \frac{1}{n^3 \sin^2n}$ converge or diverge?
149240
Divergence of a series
14031
Why does the series $\sum_{n=1}^\infty\frac1n$ not converge?
24575
How to prove that $ \sum_{n \in \mathbb{N} } | \frac{\sin( n)}{n} | $ diverges?
107619
Suppose $\sum a_n$ converges absolutely and $\sum b_n$ converges. Give an example where the Cauchy product does not converge absolutely.
3735
If $\sum_{1}^{\infty}(a_n)^3$ diverges, does $\sum_{1}^{\infty}(a_n)$?
149176
True/False: $\mathop {\lim }\limits_{n \to \infty } {{{a_n}} \over {{b_n}}} = 1$ implies $\sum {{a_n},\sum {{b_n}} } $ converge or diverge together.
143263
If $\sum a_n$ is a convergent series with $S = \lim s_n$, where $s_n$ is the nth partial sum, then $\lim_{n \to \infty} \frac{s_1+...+s_n}{n} = S$
153949
Is there a "smallest" divergent sum?
27748
Convergence of $\sum \frac{a_n}{S_n ^{1 + \epsilon}}$ where $S_n = \sum_{i = 1} ^ n a_n$
4911
Suppose $a_n>0$ and $\sum_{n=1}^{\infty}{a_n}$ diverges. Determine convergence of $\sum_{n=1}^{\infty}{\frac{a_n}{s_n^2}}$, where $s_n=\sum^n a_n$.