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Math Help - Limit of a Series

  1. #1
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    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?
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  2. #2
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    Re: Limit of a Series

    Quote Originally Posted by veronicak5678 View Post
    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.
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  3. #3
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    Re: Limit of a Series

    So if it is decreasing and null, we know it converges, but how do we find the actual limit?
    Last edited by veronicak5678; August 31st 2011 at 05:06 PM.
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