1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: 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


    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Gold Member

    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 ;).
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook