pre-cal 40s june 5, 2009
DESCRIPTION
Infinite geometric sequences.TRANSCRIPT
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 ?
Artithmetic Series: The sum of numbers in an arithmetic sequence given by
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.
is the sum to the nth termn is the "rank" of the nth terma is the first term in the sequenced is the common difference
Sigma Notation: A shorthand way to write a series.
(2n - 3) is the implicit definition of the sequence
superscript 4 means keep evaluating (2n - 3) for successive integral values of n; stop when n = 4; then add all the terms
subscript n = 1 means "start with n = 1 and evaluate (2n - 3)"
Σ is capital sigma (from the greek alphabet); means sum
means (2(1) -3) + (2(2) -3) + (2(3) -3) + (2(4) -3) = -1 + 1 + 3 + 5
= 8
∑n=1
4
(2n - 3)
Example:
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
is the sum to the nth termn is the "rank" of the nth terma is the first term in the sequenced is the common difference
or
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 SERIES0 < |r| <1
DIVERGENT SERIES|r| > 1
Find the infinite sum for a geometric series given: r = 2 3
a = 12