closed form expression for the sum of the first s items of alternating binomial coefficients

Is there a closed form expression for the following sum:

$$\sum_{k=0}^s (-1)^k {n \choose k},$$

where $s \in \{0,1,2,...,n\}$

-- which is basically the first $s$ terms in the alternating binomial coefficients series. I know if $s=n$, the sum is zero, but I cannot figure out a general closed form expression in terms of $s$.

Yes there is: $$(-1)^s {n-1 \choose s}$$