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I need help finding the sum of this series

  • Thread starter Randall
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  • #1
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Homework Statement


Find the sum of the series from k=0 to infinity of ((4^k)-(3^k))/(5^k)

Homework 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

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.
 

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Answers and Replies

  • #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.
 
  • #3
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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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