How to evaluate this summation: $\sum_{i=0}^{n} 2^i$?

Question

How would I evaluate $\large\sum_{i=0}^{n} 2^i$? I'm having difficulty determining the first thing I should do.

Answer 1

HINT : Let S be the sum. $$2S=\color{red}{2^1+2^2+\cdots+2^{n-1}+2^{n}}+2^{n+1}$$ $$S=2^0+\color{red}{2^1+2^2+\cdots+2^{n-1}+2^n}$$ Then, subtract the latter from the former.

Answer 2

There is a geometric series with ratio $q=2$ $$\sum_{i=0}^{n} 2^i=\frac{1-2^{n+1}}{1-2}=2^{n+1}-1$$