Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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
    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!
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Similar Discussions: Trying to find the quotient of infinite sums
  1. Infinite sum (Replies: 6)

  2. An infinite sum (Replies: 3)