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!

Find the sum

  1. Mar 11, 2009 #1
    1. The problem statement, all variables and given/known data

    Find the sum [tex]\sum_{0}^{\infty} \frac {n^2} {3^n}[/tex]

    2. Relevant equations
    3. The attempt at a solution

    I don't know how to go about finding this sum, I have a guess of what it will be just by adding the first ten terms or so, but how do I find an actual approximation?
  2. jcsd
  3. Mar 11, 2009 #2
    Try multiplying three geometric series together and see how close it is to the above series. I think it's simmilar to repeated roots in differential equations.
  4. Mar 11, 2009 #3
    The only similar series I see here are:

    [tex]\sum_{0}^{\infty} (\frac {1} {3})^n[/tex]

    [tex] \sum_{0}^{\infty} n^2[/tex]
  5. Mar 11, 2009 #4
    Try looking at the second derivative of [tex]\sum_0^\infty x^n[/tex].
  6. Mar 11, 2009 #5


    User Avatar
    Homework Helper

    homogeneous differentiation


    that is
    Last edited: Mar 11, 2009
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Similar Discussions: Find the sum
  1. Finding the sum of (Replies: 9)

  2. Find the sum (Replies: 1)

  3. Find the Sum: (Replies: 6)

  4. Find the Sum (Replies: 2)