# Thread: convergence of a series

1. ## convergence of a series

How would I go about checking the convergence (absolute/conditional) of:

Thank you

2. Hints :

(i) Decompose:

$(\sin 3n)(\cos n)=\dfrac{1}{2}(\sin 4n+\sin 2n)$

(ii) Use the Dirichlet test.

Fernando Revilla

Tried to divid by 1/n and 1/n^2 but couldn't find a finit limit.

4. Hints :

$\sin \dfrac{1}{\sqrt{n}}\sim \dfrac{1}{\sqrt{n}}\;(n\rightarrow +\infty)$

$\log \dfrac{n+1}{n-1}=\log\left(1+\dfrac{2}{n-1}\right)\sim \dfrac{2}{n-1}\; (n\rightarrow +\infty)$

P.S. Perhaps, it should be better to open new threads for new problems. Thanks.

Fernando Revilla