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Differentiating a term n+1 times

  1. Jun 6, 2012 #1
    Differentiating the term:

    (x2-1)u' n+1 times gives (according to my book):

    (x2-1)u(n+2) + 2x(n+1)u(n+1) + n(n+1)u(n)

    Now I see how the first two parts arise. However, I don't really understand the last one - or more specifically I don't understand how you find that un appears exactly n(n+1) times. It is pretty clear that every un comes from when you have 2xun and then invoke the product rule, but how do you know that the sum of all these contributions (2 + 4 + 6 + 8 + 10).. sum up to n(n+1)?
  2. jcsd
  3. Jun 6, 2012 #2
    You could prove it by induction.
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