Abstract
This chapter discusses the basic concepts and elementary theorems of infinite series. Infinite sums present problems that finite sums do not. A finite sum can be calculated simply by applying the process of addition to the terms. This cannot be done with an infinite sum because regardless of the number of terms included in the process of addition, there are always some left over. The chapter presents one way of dealing with this problem A series that converges to a sum S is said to be a convergent series. This is a reasonable definition to give to the sum of an infinite number of terms. A convergent series may have its sum approximated to any desired degree of accuracy by taking the sum of a sufficiently large number of terms. Thus, at least for numerical work, a convergent infinite series may be replaced by one of its partial sums, the particular partial sum being dictated by the accuracy required in the problem. It is not always possible to write down a convenient expression for the sum of the first n terms of an infinite series. Hence, it is usually difficult to apply the definition directly to an infinite series to settle the question of convergence or divergence. The chapter presents some general theorems, which will help determine these facts.
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