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Homework Help: Need help with proof

  1. Apr 2, 2006 #1
    Let [tex] A_i = \frac{1}{n}\cdot \frac{(-1)^{n-i}}{i!\cdot(n-i)!} \int_{0}^{n} \frac{t(t-1)...(t-n)}{t-i}dt[/tex]

    I need to prove

    [tex] \sum_{i=0}^{n} A_i = 1 [/tex].

    I tried tinkering with the equasion but I'm really at a loss what to do with the integral. I'd appreciate any help.
     
    Last edited: Apr 2, 2006
  2. jcsd
  3. Apr 2, 2006 #2
    Error?

    Hi! Is there an error somewhere?

    I tried evaluating [tex] \sum_{i=0}^{1} A_i [/tex] but my answer was 0, and not 1. Perhaps you can re-check the question?

    All the best!
     
  4. Apr 2, 2006 #3
    Corrected now, thx :) (It's (n-i)!)
     
  5. Apr 2, 2006 #4
    Thanks for the correction, but I still can't obtain the correct answer for [tex] \sum_{i=0}^{1} A_i [/tex]. Puzzling...
     
  6. Apr 2, 2006 #5
    In the sum i goes from 0 to n. And it's (-1)^(n-i). Sorry for the mistakes.
     
    Last edited: Apr 2, 2006
  7. Apr 2, 2006 #6
    Well, the Binomial Series is probably involved... seeing the factorials and the term [tex] (-1)^{n-i} [/tex], but apart from that, I am not very sure how to proceed...
     
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