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

mathman

I don't believe there is any such formula.

3. Oct 14, 2007

sutupidmath

well, i think there is one, because as long as i remember i have seen it in a textbook, but it is quite long i think, and i cannot remember how it was right now. I am gonna look at it.

4. Oct 14, 2007

atqamar

Last edited: Oct 14, 2007
5. Oct 15, 2007

mathman

Your answer 2n is for s=n, the original question was for s<n.

6. Oct 15, 2007

Count Iblis

No formula exists in this case. See the book A=B for how to simplify binomial summations. There exists simple algorithms that will yield a formula or will tell you that no formula exists.