1. ## Alternating series

Hi everyone,

how do i find if the series converges absolutely or conditionally.
i need help with these question.

Test the alternating series for convergence or divergence.
i) $\displaystyle \sum^\infty _{n=1}$$\displaystyle \frac {(-1)^{(n-1)}}{n^\frac {1}{2}}$

my working, by expanding,
1>0.7071>0.577

The series converges.
* i need to find the limit to confirm, how do i do this? is it
$\displaystyle limit \frac {1}{n^\frac{1}{2}} = 0$

thank you for all your help.

2. By Leibniz test, the series converges.

Now, in order to study its conditional or absolute convergence, recall the following: if $\displaystyle \sum a_n<\infty$ but $\displaystyle \sum|a_n|=\infty,$ then the series converges conditionally. If $\displaystyle \sum a_n<\infty$ and $\displaystyle \sum|a_n|<\infty,$ then the series converges absolutely.

3. thank you for helping to clarify, but i need to prove it in the equation, need someone to guide me.

thank you for help & guidance, really need more help on this...

4. i gave you the tools to do so!