1964 AHSME Problems/Problem 31
Revision as of 16:49, 5 March 2014 by Bobthesmartypants (talk | contribs) (Created page with "Let <cmath>f(n)=\dfrac{5+3\sqrt{5}}{10}\left(\dfrac{1+\sqrt{5}}{2}\right)^n+\dfrac{5-3\sqrt{5}}{10}\left(\dfrac{1-\sqrt{5}}{2}\right)^n.</cmath> Then <math>f(n+1)-f(n-1)</math>,...")
Let ![\[f(n)=\dfrac{5+3\sqrt{5}}{10}\left(\dfrac{1+\sqrt{5}}{2}\right)^n+\dfrac{5-3\sqrt{5}}{10}\left(\dfrac{1-\sqrt{5}}{2}\right)^n.\]](http://latex.artofproblemsolving.com/b/5/1/b5166380b2f27d633122cb1fcf941cb3b030aca3.png)
Then 
, expressed in terms of 
, equals:
