2007 AMC 12B Problems/Problem 15
Revision as of 15:19, 20 February 2008 by Chickendude (talk | contribs) (New page: ==Problem 15== The geometric series <math>a+ar+ar^2\cdots</math> has a sum of <math>7</math>, and the terms involving odd powers of <math>r</math> have a sum of <math>3</math>. What is <ma...)
Problem 15
The geometric series has a sum of
, and the terms involving odd powers of
have a sum of
. What is
?
Solution
The sum of an infinite geometric series is given by where
is the first term and
is the common ratio.
In this series,
The series with odd powers of is given as
It's sum can be given by
Doing a little algebra