Simplification of sum of exponentials?

Question

Is there a way to simplify the expression $\sum _{k=0}^n 2^k$? That is, is there a way to write it without a $\sum$ or $\prod$ operator?

Answer 1

$$1 + 2 + 4 + \cdots 2^n = 11 \cdots 1_\text{binary}=2^{n+1}-1$$

In general, $\sum_{k=0}^n a^n$ is a geometric series.