ABSTRACT
In mathematics a sequence and a series are not the same thing. Roughly speaking, a sequence is an ordered list whereas a series is the (formal) sum of terms in a sequence. This chapter explores the sequence of partial sums graphically and numerically. It discusses the basic properties of convergent series and shows that the question of convergence of a series cannot be so easily settled; there are many divergent series whose terms have limit zero. The chapter examines a series that diverge slowly by using partial sums of the harmonic series. It proves the convergence or divergence of a series by relating its terms to those of another series whose convergence or divergence is known. The chapter examines decimal representations of rational numbers, and discusses how to represent real numbers with respect to bases other than 10. It also includes exercise problems related to the concept of series.
