Would the following series be convergent or divergent.


I applied the root test to the following series and got.


I got $\lim$ $k\rightarrow\infty$


using Le Hospitals rule I got


which is zero

0<1 convergent?

  • $\begingroup$ Except for a constant in the denominator after applying l'Hopital's rule (which doesn't change the limit), it looks good. $\endgroup$ – Clayton Nov 8 '13 at 18:50

Correct limit and correct conclusion; you simply have a slight error in the derivative of the denominator, $(3^k)' = (\log 3)3^k$.

  • $\begingroup$ Oh yes that makes sense $\endgroup$ – Fernando Martinez Nov 8 '13 at 18:58

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