# Alternating series

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• Feb 5th 2010, 03:04 AM
anderson
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.
• Feb 5th 2010, 04:32 AM
Krizalid
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.
• Feb 5th 2010, 06:31 AM
anderson
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...
• Feb 5th 2010, 07:43 AM
Krizalid
i gave you the tools to do so!

show your progress. :D