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Help with determining if a series is convergent or divergent question

  1. Apr 3, 2014 #1
    1. The problem statement, all variables and given/known data

    Problem is attached in this post.

    2. Relevant equations

    Problem is attached in this post.

    3. The attempt at a solution

    I know how to find the sum of this series, but I don't know what method to use in order to prove that this series converges. Also I don't understand how I'm supposed to tell as to whether or not this is a geometric series.
     

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  2. jcsd
  3. Apr 3, 2014 #2

    Dick

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    It's not geometric because the ratio of consecutive terms isn't a constant, but that ratio does approach a limit. Is that enough of a clue?
     
  4. Apr 3, 2014 #3
    Would the limit have to be 0 for the series to convergent?

    Lim (3^n + 4^n)/(7^n) n -> ∞ = 0 For the series to be convergent? (I actually tried this, but can't seem to find a method to solve for such a limit).
     
    Last edited: Apr 3, 2014
  5. Apr 3, 2014 #4

    Dick

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    You mean Lim (3^n + 4^n)/(7^n) n -> ∞ = 0. You should be able to. Divide numerator and denominator by 7^n. But that's not what I'm talking about. I'm talking about the ratio ##\frac{a_{n+1}}{a_n}##.
     
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