0
$\begingroup$

Consider the series $$\sum_{n=1}^\infty \frac{-3n(-3)^nx^n}{(n+1)\sqrt n} $$

For which real numbers $x$ does this series converge absolutely? converge conditionally? diverge?

How do I tackle these types of problems, where do I start? All I noticed is that I could perhaps use L.A.S.T. to find values of $x$ such that the series converges conditionally.

$\endgroup$

closed as off-topic by Did, Cesareo, Rebellos, user416281, rtybase Nov 11 '18 at 15:19

This question appears to be off-topic. The users who voted to close gave this specific reason:

  • "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Did, Cesareo, Rebellos, Yanko, rtybase
If this question can be reworded to fit the rules in the help center, please edit the question.

  • $\begingroup$ need help on editing denominator meant to be square toot of n $\endgroup$ – Rivaldo Nov 10 '18 at 15:53
2
$\begingroup$

HINT

Use root test to obtain the condition $3|x|<1$ and then study the limit cases a part.

$\endgroup$

Not the answer you're looking for? Browse other questions tagged or ask your own question.