Evaluate $\sum_{j=0}^{k} (-1)^{j} \binom{n}{j}$

Question

I want to evaluate

$$\sum_{j=0}^{k} (-1)^{j} \binom{n}{j}$$

obviously if $k$ goes up to $n$ then this is quite a common question. My question is how to deal with this question when the sum is truncated (stops at $k \le n$?

Do we use the answer for $n=k$ and the fact that there's some symmetry in binomial coefficients? (that is, $\binom{n}{k} = \binom{n}{n-j}$?)

any help hugely appreciated.

Mark