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The problome is rewriten here: $\sum_{i=0}^k \frac{((i-k)a)^i b^{k-i}}{i!}$ where $0, k is an integer larger than 1.

I came to this equation when i try to find some probability. I have tried some formulas on permutation and combination, fractional, but with little improvement.

I hope you can give me some sugestions! Thanks a lot!

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    What is the question? How do you want to simplify this?2012-10-29
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    It is equivalent to $\sum_{i=0}^k\prod_{j=1}^i (1-\frac{k}{i})a$. Is this helpful?2012-10-29
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    I want to get an expression without factorials or \sum operations.2012-10-29
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    Does [] mean floor or brackets?2012-10-29
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    They are only brackets. I have replaced [] with ().2012-10-29
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    Since it is a finite sum, try writing the first few terms and the last few terms, perhaps there is some simplification.2012-10-29

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