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Sum of power series

  1. Nov 29, 2011 #1
    I have to find the sum of the power series: [tex]\sum_{n=1}^\infty nx^{n+1}[/tex]

    I know the I'm supposed to show work but I don't have any idea where to start. I'm not asking for you to do the problem for me, just a hint.

    The only idea I had was to take the derivative to get rid of the n+1 in the exponent but I'm not sure if [tex]\sum_{n=1}^\infty n(n+1)x^{n}[/tex] is any easier to solve.

    Also I tried looking at the integral but again didn't see what to do
    [tex]\sum_{n=1}^\infty \frac{nx^{n+2}}{n+2}[/tex]

    Thank you.
     
  2. jcsd
  3. Nov 29, 2011 #2
    Try factoring out [itex]x^2[/itex] and see if the resulting series reminds you of something familiar.
     
  4. Nov 29, 2011 #3
    So then I would have:

    [tex]x^2\sum_{n=1}^\infty nx^{n-1}[/tex]

    That doesn't look familiar.. should it?
     
  5. Nov 29, 2011 #4

    SammyS

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    Integrate [itex]\displaystyle nx^{n-1}[/itex]
     
  6. Nov 29, 2011 #5
    I guess I just need more practice with these. Thank you, I don't think I would have thought of that any time soon ;).
     
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