Advanced Engineering Mathematics, 7th Edition

19.1 Sequences and Series

INTRODUCTION

Much of the theory of complex sequences and series is analogous to that encountered in real calculus. In this section we explore the definitions of convergence and divergence for complex sequences and complex infinite series. In addition, we give some tests for convergence of infinite series. You are urged to pay special attention to what is said about geometric series since this type of series will be important in the later sections of this chapter.

Sequences

A sequence {z_n} is a function whose domain is the set of positive integers; in other words, to each integer n = 1, 2, 3, . . ., we assign a complex ...