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Homework Help: Not able to simplify this summation formula?

  1. Jan 10, 2014 #1

    Please see the attached pdf file. Equation 1 and equation 2 are equivalent.
    Can someone please help me understand how to simplify equation 1 to get to equation 2?


    Attached Files:

    Last edited: Jan 10, 2014
  2. jcsd
  3. Jan 10, 2014 #2


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    The summation variable is n, so x can be considered a constant hence it can be pulled out the front.

    What is


    equal to?
  4. Jan 10, 2014 #3
    Please see the new attached file.
    This is how far I could go.

    Attached Files:

  5. Jan 10, 2014 #4


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    The point is that both of your series are geometric series. What you do in your last post is essentially repeating the proof that the sum of the geometric series, [itex]\sum_{n=0}^\infty r^n[/itex] is [itex]\frac{1}{1- r}[/itex] except that you have [itex]r= \frac{1}{\gamma}[/itex].
  6. Jan 10, 2014 #5


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    There is no mention of infinite sums.

    musicgold, so what is


    And hence, let n=10. Also,


    Can be simplified further. At least get rid of the fraction within the denominator.
  7. Jan 10, 2014 #6
    Please see the attached file.

    I think, I am close, but not sure how to get rid of the 'y' in the encircled term.
    What am I missing?

    Attached Files:

  8. Jan 10, 2014 #7


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    Sorry, this was supposed to be


    We're looking for


    while you're finding


    In your second attachment when you found


    You began the sum with n=0 when you should've began with n=1.
  9. Jan 15, 2014 #8

    Yes. I was able to solve it with that correction. See attached. Thank you very much.

    Attached Files:

  10. Jan 16, 2014 #9


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    Good work :smile:
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