Difference between revisions of "Mock AIME 1 2006-2007 Problems/Problem 9"

Revision as of 10:41, 30 September 2006

Let $a_{n}$ be a geometric sequence of complex numbers with $a_{0}=1024$ and $a_{10}=1$ , and let $S$ denote the infinite sum $S = a_{10}+a_{11}+a_{12}+...$ . If the sum of all possible distinct values of $S$ is $\frac{m}{n}$ where $m$ and $n$ are relatively prime positive integers, compute the sum of the positive prime factors of $n$ .

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 ==Problem==
-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>.
+===Revised statement===
+Let <math>a_{n}</math> be a [[geometric sequence]] of [[complex number]]s with <math>a_{0}=1024</math> and <math>a_{10}=1</math>, and let <math>S</math> denote the [[infinite]] sum <math>S = a_{10}+a_{11}+a_{12}+...</math>. If the sum of all possible [[distinct]] values of <math>S</math> is <math>\frac{m}{n}</math> where <math>m</math> and <math>n</math> are [[relatively prime]] [[positive integer]]s, compute the sum of the positive [[prime number | prime]] [[divisor | factors]] of <math>n</math>.
+===Original statement===
 ==Solution==
 {{solution}}
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 *[[Mock AIME 1 2006-2007]]
+[[Category:Intermediate Complex Numbers Problems]]