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Trying to find the quotient of infinite sums

  1. Feb 7, 2012 #1
    i am trying to re-express the following in terms of a rational function: [itex]\frac{(0+x+2x^2+3x^3+...)}{1+x+x^2+x^3+...} [/itex]. i know that this is supposed to be [itex]\frac{1}{x-1}[/itex] but I can't figure out how to do it.

    I know the denominator is just [itex] \frac{1}{1-x}[/itex]. so in order for this work out, the infinite sum which makes up the numerator should be [itex]\frac{1}{(1-x)(x-1)}[/itex]. so my problem is figuring out how to express [itex]0+x+2x^2+3x^3+...[/itex] as a function of x. I have tried integrating/differentiating the series which didn't work and i haven't been able to figure out another way to do this.

    can someone help me figure this out?
     
  2. jcsd
  3. Feb 7, 2012 #2

    micromass

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    Factor x out first, then integrate.
     
  4. Feb 8, 2012 #3
    oh wow I am really getting rusty on my calculus. thanks for your reply!
     
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