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Homework Help: Closed Form of an Infinite Series

  1. Nov 13, 2007 #1
    1. The problem statement, all variables and given/known data

    I'm looking to find a closed form for the infinite series:
    1*C(n,1) + 2*C(n,2) + 3*C(n,3) + ... + n*C(n,n)

    2. Relevant equations

    C(n,k) = n!/(k!*(n-k)!)
    C(n,1) + C(n,2) + C(n,3) + ... + C(n,n) = 2^n - 1

    3. The attempt at a solution

    I'm not quite sure where to start this problem. Any tips?
  2. jcsd
  3. Nov 13, 2007 #2


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    (1+x)^n=C(0,n)+C(1,n)*x+C(2,n)*x^2+...+C(n,n)*x^n. This is why it's clear that your second identity is pretty obvious (put x=1). Think what happens when you differentiate that wrt x and then put x=1. Oh, and your series really isn't that infinite, is it?
    Last edited: Nov 13, 2007
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