ABSTRACT
In this section we will use standard summation notation:
aj ≡ am + am+1 + · · ·+ an .
A series is an infinite sum. One of the most effective ways to handle an infinite process in mathematics is with a limit. This consideration leads to the following definition:
Definition 3.1 The formal expression
aj ,
where the ajs are real or complex numbers, is called a series. ForN = 1, 2, 3, . . . , the expression
SN =
aj = a1 + a2 + . . . aN
is called the Nth partial sum of the series. In case
lim N→∞
SN
exists and is finite we say that the series converges. The limit of the partial sums is called the sum of the series. If the series does not converge, then we say that the series diverges.
