# Limit of a Series

• 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 + ...

$\sum\limits_{k = 1}^\infty {\left( { - 1} \right)^{k + 1} \frac{{\left|{\pi - 6} \right|^{k+1} }}{{\pi ^k }}}$
If so, you need to show that ${\frac{{\left| {\pi - 6} \right|^{k+1} }}{{\pi ^k }}}$ is a decreasing null sequence.