key term - Geometric Series

Definition

A geometric series is a sequence of numbers in which each term after the first is found by multiplying the previous term by a fixed non-zero number called the common ratio. The sum of all these terms forms an infinite geometric series.

Related terms

Common Ratio: The common ratio refers to the fixed non-zero number that multiplies each term to get to the next one in a geometric sequence or series.

Convergent Geometric Series: A convergent geometric series is one where all its terms add up to a finite value when summed infinitely. This happens only when the absolute value of the common ratio is less than 1.

Divergent Geometric Series: A divergent geometric series occurs when adding up all its terms results in an infinite value. This happens when the absolute value of the common ratio is greater than or equal to 1.