Infinite Geometric
Series
iphone to infinity for
righty's by flickr user KIT

Given a geometric sequence in which and , what is the
value of ?

Series: The sum of numbers in a sequence to a particular term in a
sequence.
Example: denotes the sum of the first 5 terms.
denotes the sum of the first n terms.
Artithmetic Series: The sum of numbers in an arithmetic
sequence given by
is the sum to the nth term
n is the \"rank\" of the nth term
a is the first term in the sequence
d is the common difference

Sigma Notation: A shorthand way to write a series.
Example:
4
∑(2n - 3) means (2(1) -3) + (2(2) -3) + (2(3) -3) + (2(4) -3)
n=1 = -1 + 1 + 3 + 5
=8
Σ is capital sigma (from the greek alphabet); means sum
subscript n = 1 means \"start with n = 1 and evaluate (2n - 3)\"
superscript 4 means keep evaluating (2n - 3) for successive
integral values of n; stop when n = 4; then add all the terms
(2n - 3) is the implicit definition of the sequence

Series: The sum of numbers in a sequence to a particular term in a
sequence.
Example: denotes the sum of the first 5 terms.
denotes the sum of the first n terms.
Geometric Series: The sum of numbers in an geometric sequence
given by
or
is the sum to the nth term
n is the \"rank\" of the nth term
a is the first term in the sequence
d is the common difference

or

Given the geometric sequence in which and r = , which
term has a value of 27?
Find the sum of the first 5 terms.

Given the geometric sequence in which and r = , which
term has a value of 27?
Find the sum of the first 5 terms.

Infinite Geometric
Series
iphone to infinity for
righty's by flickr user KIT

Infinite Geometric Series
Why is that the formula?

CONVERGENT SERIES
0 < |r| <1
DIVERGENT SERIES
|r| > 1

Find the infinite sum for a geometric series given: a = 12 r= 2
3