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Solving some problem I have stumbled into the following sum :

$ \displaystyle \sum_{i=0}^{n-2} {e \choose i} (n-1-i) (1-p)^{e-i} p^i $

where $ 0 \leq e \leq {n \choose 2}$.

I am not very efficient with the evaluation of these sums so I would like to ask if there is any way to evaluate this sum or obtain a sharp lower bound for it?

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    Did you get something out of a solution below?2011-04-07

1 Answers 1