# Limit of a Series

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• August 30th 2011, 03:02 PM
veronicak5678
Limit of a Series
Find the limit:

(2pi-6) + [(pi -6)^2] / pi + [(pi-6)^3] / pi^2 + ...

I see that, except for the first which is positive, this is alternating between positive and negative terms, but how do I find the limit?
• August 30th 2011, 03:49 PM
Plato
Re: Limit of a Series
Quote:

Originally Posted by veronicak5678
Find the limit:
(2pi-6) + [(pi -6)^2] / pi + [(pi-6)^3] / pi^2 + ...

It seem to me that your question is about
$\sum\limits_{k = 1}^\infty {\left( { - 1} \right)^{k + 1} \frac{{\left|{\pi - 6} \right|^{k+1} }}{{\pi ^k }}}$

If so, you need to show that ${\frac{{\left| {\pi - 6} \right|^{k+1} }}{{\pi ^k }}}$ is a decreasing null sequence.
• August 30th 2011, 05:16 PM
veronicak5678
Re: Limit of a Series
So if it is decreasing and null, we know it converges, but how do we find the actual limit?