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?

Printable View

- Aug 30th 2011, 03:02 PMveronicak5678Limit 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? - Aug 30th 2011, 03:49 PMPlatoRe: Limit of a Series
It seem to me that your question is about

$\displaystyle \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 $\displaystyle {\frac{{\left| {\pi - 6} \right|^{k+1} }}{{\pi ^k }}}$ is a decreasing null sequence. - Aug 30th 2011, 05:16 PMveronicak5678Re: Limit of a Series
So if it is decreasing and null, we know it converges, but how do we find the actual limit?