1. Not finding help here? Sign up for a free 30min 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!

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...
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Need help with proof
  1. Need help on a proof (Replies: 2)

  2. Need Help On a Proof (Replies: 15)

Loading...