Help: sum of binomial coefficents

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Help: sum of binomial coefficents !

Hello!
I cannot figure out how to derive a closed formula for the sum of "the first s" binomial coefficients:

\sum_{k=0}^{s} \left({{n}\atop{k}}\right)

with s<n

Could you please help me find out some trick to derive the formula... I've an exam on monday!

Thank you very much!
 
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Oh nevermind, I misread it as the sum of n binomial coefficients.
 
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Dear Thealchemist83,

I have just read your question, long after your exam... If this was your task, I wonder about the mark you've got because this sum does not have a closed form.:smile:

See the fifth chapter of Concrete Mathematics (Graham, Knuth, Patashnik)

Istvan
 

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