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Not able to simplify this summation formula?

  1. Jan 10, 2014 #1
    Hi,

    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?

    Thanks.
     

    Attached Files:

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

    Mentallic

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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

    [tex]1+r+r^2+...+r^n[/tex]

    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

    HallsofIvy

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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

    Mentallic

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    There is no mention of infinite sums.

    musicgold, so what is

    [tex]\sum_{i=1}^{n}\frac{1}{1+y}[/tex]

    And hence, let n=10. Also,

    [tex]\frac{1-\frac{1}{\gamma^{n+1}}}{1-\frac{1}{\gamma}}[/tex]

    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

    Mentallic

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    Sorry, this was supposed to be

    [tex]\sum_{i=1}^{n}\frac{1}{(1+y)^i}[/tex]

    We're looking for

    [tex]\sum_{n=1}^{10}\frac{1}{(1+y)^n}[/tex]

    while you're finding

    [tex]\sum_{n=0}^{10}\frac{1}{(1+y)^n}[/tex]

    In your second attachment when you found

    [tex]s=\sum\frac{1}{\gamma^n}=1+\frac{1}{\gamma}+\frac{1}{\gamma^2}+...[/tex]

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

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

    Attached Files:

  10. Jan 16, 2014 #9

    Mentallic

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    Good work :smile:
     
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