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Math Help - Power Series w/ factorial

  1. #1
    Senior Member mollymcf2009's Avatar
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    Power Series w/ factorial

    Can someone check to see if I evaluated this correctly?

    \sum^{\infty}_{n+1} \frac{n!x^n}{8\cdot 17\cdot 26\cdot ...(9n-1)}

    = \sum^{\infty}_{n+1}  \frac{n!x^n}{(9n-1)!}

    Is that right?
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by mollymcf2009 View Post
    Can someone check to see if I evaluated this correctly?

    \sum^{\infty}_{n+1} \frac{n!x^n}{8\cdot 17\cdot 26\cdot ...(9n-1)}

    = \sum^{\infty}_{n+1}  \frac{n!x^n}{(9n-1)!}

    Is that right?
    no

    (9n - 1)! = (9n - 1)(9n - 2)(9n - 3)....(3)(2)(1)
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  3. #3
    Senior Member mollymcf2009's Avatar
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    Quote Originally Posted by Jhevon View Post
    no

    (9n - 1)! = (9n - 1)(9n - 2)(9n - 3)....(3)(2)(1)
    Ok, I need a hint....
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  4. #4
    Senior Member mollymcf2009's Avatar
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    Quote Originally Posted by Jhevon View Post
    no

    (9n - 1)! = (9n - 1)(9n - 2)(9n - 3)....(3)(2)(1)

    Ok, how about...9n!-1
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  5. #5
    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by mollymcf2009 View Post
    Ok, how about...9n!-1
    It doesn't work for values of n\geqslant3!! XD

    What in particular are you asked to do with this series? Show that it converges??
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  6. #6
    Senior Member mollymcf2009's Avatar
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    Quote Originally Posted by Chris L T521 View Post
    It doesn't work for values of n\geqslant3!! XD

    What in particular are you asked to do with this series? Show that it converges??
    Find the radius of convergence and the interval of convergence.

    I don't know a good way to rewrite factorials. Do I need to do that before I try to evaluate this? Thanks Chris!
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  7. #7
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by mollymcf2009 View Post
    Find the radius of convergence and the interval of convergence.

    I don't know a good way to rewrite factorials. Do I need to do that before I try to evaluate this? Thanks Chris!
    if that's the case, why not use the ratio or root test? you don't need to rewrite anything. probably the ratio test will be easier here

    however, in general, you can use Stirling's approximation.
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  8. #8
    MHF Contributor matheagle's Avatar
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    Do you mean n=1 instead of n+1?
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