Hello,

I have the following sequence:

$\displaystyle a_{n}=\frac{1}{\ln(x)}$ when n is even

$\displaystyle a_{n}=-\frac{1}{\ln(x)}$ when n is uneven

I want to determine whether the sequence is absolute convergent, divergent or conditional convergence.

I have tried showing that the sequence is absolute covergent by showing that $\displaystyle \sum_{2}^{\infty} \vert a_{n} \vert$ is convergent. I tried using the integral test but I ended up with a strange expression (which contains li(x)).

I have also tried using the ration test which leads to no conclusion.

Suggestions would be appreciated.

Thanks