Help: sum of binomial coefficents

[thealchemist83]

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!

 

[kaotak]

Oh nevermind, I misread it as the sum of n binomial coefficients.

 

[Istvan Mezo]

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.

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

Istvan