OK, questions is about divergent, conditionally convergent, or abs convergent.

$\displaystyle

\sum\limits_{n = 1}^\infty {\frac{{\left( { - 1} \right)^{\left\lfloor {\sqrt n } \right\rfloor } }}{n}}

$

the first few terms are as follows,

-1, -1/2, -1/3, 1/4, 1/5, 1/6, 1/7, 1/8, -1/9......

I know I should take into the case of positive and negative terms by themselves. Using the epsilon/delta definition would also help. Thanks

EDIT: Sorry about mixing the variables guys, been a long day