[i]Geometric series[/i] are series of the form [br] [math]a+ar+ar^2+ar^3+\cdots+ar^{n-1}+\cdots=\sum_{n=1}^{\infty}ar^{n-1}[/math][br]in which [math]a[/math] and [math]r[/math] are fixed real numbers and [math]a\ne0[/math]. The parameter [math]r[/math] is the [i]ratio [/i]of the series.[br]If [math]\left|r\right|<1[/math], then the series converges to the real number [math]\frac{a}{1-r}[/math]. If [math]\left|r\right|\ge1[/math], then the series diverges.[br][br]In this interactive figure, the sum of the series is seen as the total signed area of the rectangles.

[i]Developed for use with Thomas' Calculus, published by Pearson.[/i]