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Summation of a Product of Functions

  1. May 19, 2012 #1
    Is there a general formula for something like

    [itex]\sum_{n=0}^{\infty} \left( f(n) \times g(n) \right)[/itex]



    For example, what is

    [itex]\sum_{n=0}^{\infty} \left( 3^n \times \frac{n!}{n^2} \right)[/itex]
     
  2. jcsd
  3. May 19, 2012 #2

    micromass

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    Infinity, since the series diverges.
     
  4. May 20, 2012 #3

    Stephen Tashi

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