Precalculus (6th Edition) Blitzer

A geometric sequence with limited terms consists of values in the form of $a_1, a_1r, a_1r^2,, a_1r^{n-1}$ with $n$ as a positive integer. On the other hand, an infinite geometric series will contain an unlimited number of values; that is $n\to \infty$. The formulas for the summation of the two series are different.