August 25th, 2008, 04:44 AM
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 | Flow Master | | Join Date: Dec 2007 Location: Zeitgeist
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Quote:
Originally Posted by Number Cruncher 20  Hi,
I have been asked to derive a simple closed form expression for the
following sum:
n
∑ (-1)^(m+i) *(nCi)*(iCm) = S n, m
i = m
[with m = 0,1,2,....,n ; n= 0,1,2,....] and C is the combinations symbol.
I know that we are meant to be using the binomial theorem but I dont quite know where to go from there. Any help would be much appreciated. | Three hints:
1. Prove that  is equal to zero if  and is equal to 1 if  .
2. Prove that  for  .
3. Deduce from 1. and 2. that your expression is equal to zero if  and is equal to 1 if  .
__________________ There are two things you should never try to prove: the impossible and the obvious. The greater danger for most of us lies not in setting our aim too high and falling short; but in setting our aim too low and achieving our mark. (Michelangelo Buonarroti)
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