A geometric series is the sum of the terms of a geometric sequence, where each term after the first is found by multiplying the previous term by a fixed, non-zero number called the common ratio.
5 Must Know Facts For Your Next Test
A geometric series can be finite or infinite.
The sum of a finite geometric series can be calculated using the formula $S_n = a \frac{1-r^n}{1-r}$ where $a$ is the first term, $r$ is the common ratio, and $n$ is the number of terms.
If $|r| < 1$, an infinite geometric series converges to $\frac{a}{1-r}$.
If $|r| \geq 1$, an infinite geometric series diverges.
Geometric series are used in various applications including finance for calculating compound interest.