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208 Chapter Three

IYnite series
An infinite series consistð of the elementð of an infinite sequence
arranged in a specifi order, separated by addition symbols:

a a a ... a ...
3
n
2
1
or
a a a ... a ...
1
2
0
n
Positive iYnite series
A positive infinite series is the sum of an infinite sequence, all
of whose termð are real numberð greater than zero.

Negative iYnite series
A negative infinite series is an the sum of an infinite sequence,
all of whose termð are real numberð less than zero.

Alternating iYnite series
An alternating infinite series is the sum of an infinite sequence
of positive and negative termð such that, if a and a n 1 are suc-
n
cessive terms, the following statementð hold:

If a 0, then a n 1 0
n
If a 0, then a n 1 0
n

Partial su
The partial sum S of an infinite serieð is the sum of itð first n
n
terms:

S a a a ... a n
3
2
n
1
ConvergenŁ iYnite series
A convergent infinite series is an infinite serieð whose partial
sum S approacheð a specifi finite number S as n increaseð
n
without bound: