Explain how to find the sum of a finite geometric series.

To find the sum of a finite geometric series, use the formula S_n = a(1-r^n)/(1-r), where a is the first term, r is the common ratio, and n is the number of terms.

First, identify the values of a, r, and n in the given series. Then, substitute these values into the formula and simplify.

For example, consider the series 2, 4, 8, 16, 32. Here, a = 2, r = 2 (since each term is twice the previous term), and n = 5 (since there are 5 terms).

Using the formula, S_n = a(1-r^n)/(1-r) = 2(1-2^5)/(1-2) = 2(-31)/(-1) = 62.

Therefore, the sum of the series 2, 4, 8, 16, 32 is 62.

It is important to note that the formula for the sum of a finite geometric series only works if the common ratio is not equal to 1. If the common ratio is 1, then the series is simply a sequence of the same number repeated n times, and the sum is n times that number.