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