Mock AIME 1 Pre 2005 Problems/Problem 13
Problem
A sequence 
obeys the recurrence 
for any integers 
. Additionally, 
and 
. Let ![\[S =\sum_{i=0}^{\infty}\frac{R_{i}}{2^{i}}\]](http://latex.artofproblemsolving.com/d/1/9/d19b0ce756324b08284c4c9084c64764baf2fa55.png)
can be expressed as 
for two 2 relatively prime numbers 
and 
. Determine the value of 
Solution
First, we consider the fact that
Now, consider the fact that
Thus,
and
and
Adding these together we get that
Since 420 and 23 are relatively prime we find that the answer is 
