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Homework Help: Series/binomial/multinomial theorum

  1. Sep 27, 2007 #1
    1. The problem statement, all variables and given/known data

    for any positive interget n determine

    a) SUM(from i=0 to n) of

    (-1)^i
    i!(n-i)!

    b) SUM (from i=0 to n) of

    1
    i!(n-1)!

    2. Relevant equations



    3. The attempt at a solution

    a) well i didnt realyl know how to start. i found that with
    n=1 then it becomes 1+1
    n=2 .5+1+.5
    n=3 1/3! + .5 +.5 +1/3!
    n=4 1/4! +1/3! +.25 +1/3! +1/4!
    n=4 1/5! +1/4! +.083333 +.083333 +1/4! +1/5!

    so i guess what i need is how do i get the middle term?
    or am i going about it wrong?

    for b) i know the sum is always 0, because ichecked it on my calculator. but i don't know hwo to prive that
     
  2. jcsd
  3. Sep 27, 2007 #2

    Avodyne

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    Science Advisor

    Do you know what the binomial expansion of (1+x)n is?
     
  4. Sep 27, 2007 #3
    i acctulay think i got it
    a) 2^n/n!
     
  5. Sep 28, 2007 #4

    Avodyne

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    Science Advisor

    Yes. Do the binomial expansion of (1+x)n, and the set x=1 or -1 to get the two versions of your problem.
     
  6. Sep 28, 2007 #5
    so is the 2^n/n! right?
    i get the same answer doing that as i do doing it long form (calculator)

    (mind helping on my other post ? :P)
     
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