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Homework Help: Infinite sums/series

  1. Mar 23, 2010 #1
    1. The problem statement, all variables and given/known data
    Figuring out an infinite sum question for the kid I tutor... it's late and my brain's not functioning well. I think I'm overcomplicating the question, but I can't figure it out.

    The the sum of the following infinite series:
    S = 1+3x+5x^2+...

    2. Relevant equations

    3. The attempt at a solution
    I got that tn = [tex](2n-1)x^{n-1}[/tex]

    Which means the sum is
    [tex]\Sigma (2n-1)x^{n-1}=2\Sigma nx^{n-1} - \Sigma x^{n-1} = 2\Sigma nx^{n-1} - \frac{1}{1-x}[/tex]

    And here is where I get stuck...
     
  2. jcsd
  3. Mar 23, 2010 #2

    tiny-tim

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    Hi muso07! :smile:

    Hint (for ∑ nxn-1):

    integrate. :wink:
     
  4. Mar 23, 2010 #3
    Hm, the kid's in Year 11 so he hasn't done integration yet...

    But when you integrate, you get x^n. Then [tex]lim_{(a\rightarrow\infty)} [x^{n}]^{a}_{1}= lim_{(a\rightarrow\infty)}x^{a}-x=-x[/tex]
    This isn't right, though... I feel like such an idiot. :P
     
  5. Mar 23, 2010 #4

    tiny-tim

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    (have a sigma: ∑ and an infinity: ∞ and try using the X2 and X2 tags just above the Reply box :wink:)

    No, you want d/dx lima->∞ (∑xn) :smile:
     
  6. Mar 23, 2010 #5
    You beat me to replying. Is the sum (1+x)/(1-x)^2?
     
    Last edited: Mar 23, 2010
  7. Mar 23, 2010 #6
    Nevermind, I'm just going to tell him to believe me and it shall be great.

    Thanks for all your help!
     
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