ABSTRACT
This chapter provides a brief review of infinite series with an emphasis on power series, along with a brief discussion of using complex variables in these series. In the language of mathematics, an infinite series is a summation with infinitely many terms. The usefulness of an infinite series usually depends on whether it actually adds up to some finite value. The chapter describes the geometric series which are unusual in that rather simple formulas can be derived for their partial sums. If a series converges but is not absolutely convergent, then it is converging because each term “cancels out” some of the previous terms, and the series is said to be conditionally convergent. The radius of convergence for a given power series can sometimes be determined through careful use of the formulas in either the limit ratio test or the limit root test. The chapter also provides a straightforward extension of a basic formula for computing products of polynomials.
