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.


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

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


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


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