This week in math I learned about infinite geometric sequences, series, and their respective formulas and graphing. There are two different kinds of infinite geometric sequences and series: converging and diverging.

For a diverging geometric series, the sum is infinite, and thus the graph will constantly grow. No matter the numbers, any diverging series has a ratio greater than 1 or less than -1, and will always have no sum. Graphs for diverging series’ look like this:

For a converging geometric series, the sum is . The ratio must always be less than 1 and greater than -1, and because of this, the graph will always get smaller, with the sum being finite. This is a graph for a converging series: