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I need help finding the sum of this series

  1. Jan 2, 2015 #1
    1. The problem statement, all variables and given/known data
    Find the sum of the series from k=0 to infinity of ((4^k)-(3^k))/(5^k)

    2. Relevant equations
    I'm not sure exactly. I know the test for divergence is if lim n approaches infinity of the function from m=1 to infinity does not equal 0 then the series cannot diverge

    3. The attempt at a solution
    see attached but really my work is a lame attempt at a test for divergence, and not so much an attempt at the sum. Please I need help finding the sum.
     

    Attached Files:

  2. jcsd
  3. Jan 2, 2015 #2

    PeroK

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    You're overlooking something very simple. It's difficult to give a hint without giving away the answer. Just think of the simplest thing you can do with the terms.
     
  4. Jan 2, 2015 #3
    Ahhhh. I see. This is simply the sum of two different geometric series - one with a ratio of 4/5 and one with a ratio of 3/5, yes? I feel silly now
     
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