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Thread: [SOLVED] Power Series - technical question

  1. #1
    Senior Member mollymcf2009's Avatar
    Jan 2009
    Charleston, SC

    [SOLVED] Power Series - technical question

    I understand how to do all of this, but I have a question about one part:

    Find the radius of convergence and the interval of convergence for:

    $\displaystyle \sum^{\infty}_{n=1} \frac{n!x^n}{7\cdot 15 \cdot 23 \cdot ... (8n -1)}$

    Did the ratio test:

    $\displaystyle \lim_{n \rightarrow \infty} |x| \frac{n+1}{8n+7}$

    ***Here is where I am confused...what happens to this when I take this limit?

    I think it is:
    $\displaystyle \lim_{n \rightarrow \infty} |x| \frac{n+1}{8n+7}$ = $\displaystyle |x| \frac{1}{8} $

    but I'm not sure, and I don't really understand why it would or would not be
    $\displaystyle \frac{1}{8}$

    ...How do I evaluate this part and can someone show me the process? Thanks!!

    ****NEVERMIND!!!! I see it!
    Last edited by mollymcf2009; Apr 20th 2009 at 05:14 PM.
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