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An infinite series question

  1. Apr 29, 2010 #1
    1. The problem statement, all variables and given/known data

    Rewrite the given expression as a sum whose generic term involves xn

    [m=2 to ∞] ∑m(m-1)amxm-2 + [k=1 to ∞] x∑kakxk-1

    2. Relevant equations

    None in this problem

    3. The attempt at a solution

    To make the first part involve only xn, I can use the substitution n=m-2.

    [n=0 to ∞] ∑(n+2)(n+1)an+2xn.

    But I can't make the second part in terms of xn and [n=0 to ∞], as far as I know.

    [k=1 to ∞] x∑kakxk-1 = [k=1 to ∞] ∑kakxk = [n=1 to ∞] ∑nanxn

    If I try to take change the start of the sum to n=0, that will effect the xn. See what I'm saying? I want to combine this into one big sum from n=0 to ∞.
  2. jcsd
  3. Apr 29, 2010 #2

    D H

    User Avatar
    Staff Emeritus
    Science Advisor

    So don't do that then. At this stage you have two series, both of which are in terms of xn. The only problem is one starts at n=0 while the other starts at n=1. Can you make them start at the same point?
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