ABSTRACT
A series is an infinite sum. The only way to handle an infinite process in mathematics is with a limit. This consideration leads to the following definition:
Definition 4.1 The formal expression
aj ,
where the ajs are real or complex numbers, is called a series. For N = 1, 2, 3, . . ., the expression
SN = N∑ j=1
aj = a1 + a2 + . . . aN
is called the N th partial sum of the series. In case
lim N→∞
SN
exists and is finite we say that the series converges. Otherwise we say that the series diverges.
