Sum of a series of a number raised to incrementing powers How would I estimate the sum of a series of numbers like this:  $2^0+2^1+2^2+2^3+\cdots+2^n$.  What math course deals with this sort of calculation?  Thanks much!

late to the party but i think it's useful to have a way of getting to the general formula.
this is a geometric serie which means it's the sum of a geometric sequence (a fancy word for a sequence where each successive term is the previous term times a fixed number). we can find a general formula for geometric series following the logic below
$$
a = \text{firstterm}\\
r = \text{common ratio}\\
n = \text{number of terms}\\
S_n = \text{sum of first n terms}\\
S_n = a + ar + ar^2 + \dots+ar^{n-1}\\
\\
\\
-rS_n = -ar-ar^2-ar^3 - \dots-ar^{n}\\
S_n-rS_n = a + ar + ar^2 + \dots+ar^{n-1}-ar-ar^2-ar^3 - \dots-ar^{n}\\
S_n-rS_n =a-ar^n = a(1-r^n)\\
S_n(1-r) = a(1-r^n)\\
S_n = \frac{a(1-r^n)}{(1-r)}
$$
then using a = 2
$$
S_n = \frac{1(1-2^n)}{(1-2)} = 2^n-1
$$
