Sum of a Finite Geometric Series in Alternative Form

Sum of a Finite Geometric Series in Alternative Form

## Formula

For:

$$S_n=a+ar+\cdots+ar^{n-1}$$

multiplying by $$r$$:

$$rS_n=ar+ar^2+\cdots+ar^n$$

Subtracting:

$$(1-r)S_n=a(1-r^n)$$

Therefore:

$$S_n=\frac{a(1-r^n)}{1-r}$$

for:

$$r\ne1$$

## Usage

- Used to derive or quickly evaluate finite GP sums.