Understanding Digital Signal Processing, Second Edition

Appendix B. Closed Form of a Geometric Series

In the literature of digital signal processing, we often encounter geometric series expressions like

Equation B-1. 

or

Equation B-2. 

Unfortunately, many authors make a statement like “and we know that,” and drop Eqs. (B-1) or (B-2) on the unsuspecting reader who's expected to accept these expressions on faith. Assuming that you don't have a Ph.D. in mathematics, you may wonder exactly what arithmetic sleight of hand allows us to arrive at Eqs. (B-1) or (B-2). To answer this question, let's consider a general ...