# Help: sum of binomial coefficents

1. Oct 11, 2007

### 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!!!

2. Oct 11, 2007

### kaotak

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

Last edited by a moderator: Oct 11, 2007
3. Jun 1, 2009

### Istvan Mezo

Re: Help: sum of binomial coefficents !!

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