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Thread: Generating functions problem (stuck)

  1. November 29th 2010, 07:32 PM #1
    guyonfire89
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    Generating functions problem (stuck)

    From the integers:1,3 ,9,27,81,243,729...
    I have:

    The sum from k=0 to infin of 3^k times x^k.

    How do I incorporate the geometric series into this and finish this problem?
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  2. November 29th 2010, 11:04 PM #2
    CaptainBlack
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    Quote Originally Posted by guyonfire89 View Post
    From the integers:1,3 ,9,27,81,243,729...
    I have:

    The sum from k=0 to infin of 3^k times x^k.

    How do I incorporate the geometric series into this and finish this problem?
    \displaystyle \sum_{k=0}^{\infty}3^kx^k=\sum_{k=0}^{\infty}(3x)^ k

    So if 3x<1 you have a convergent infinite geometric series.

    CB
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