Difference between revisions of "Mock AIME 1 2006-2007 Problems/Problem 9"
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===Original statement=== | ===Original statement=== | ||
− | + | Let <math>a_{n}</math> be a geometric sequence for <math>n\in\mathbb{Z}</math> with <math>a_{0}=1024</math> and <math>a_{10}=1</math>. Let <math>S</math> denote the infinite sum: <math>a_{10}+a_{11}+a_{12}+...</math>. If the sum of all distinct values of <math>S</math> is <math>\frac{m}{n}</math> where <math>m</math> and <math>n</math> are relatively prime positive integers, then compute the sum of the positive prime factors of <math>n</math>. | |
==Solution== | ==Solution== |
Revision as of 10:42, 30 September 2006
Problem
Revised statement
Let be a geometric sequence of complex numbers with
and
, and let
denote the infinite sum
. If the sum of all possible distinct values of
is
where
and
are relatively prime positive integers, compute the sum of the positive prime factors of
.
Original statement
Let be a geometric sequence for
with
and
. Let
denote the infinite sum:
. If the sum of all distinct values of
is
where
and
are relatively prime positive integers, then compute the sum of the positive prime factors of
.
Solution
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