Difference between revisions of "1964 AHSME Problems/Problem 31"
(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>,...") |
|||
| Line 3: | Line 3: | ||
Then <math>f(n+1)-f(n-1)</math>, expressed in terms of <math>f(n)</math>, equals: | Then <math>f(n+1)-f(n-1)</math>, expressed in terms of <math>f(n)</math>, equals: | ||
| − | <math>\textbf{(A) }\frac{1}{2}f(n)\qquad\textbf{(B) }f(n)\qquad\textbf{(C) }2f(n)+1\qquad\textbf{(D) }f^2(n)\qquad \textbf{(E) }\frac{1}{2}(f^2(n)-1)</math> | + | <math>\textbf{(A) }\frac{1}{2}f(n)\qquad\textbf{(B) }f(n)\qquad\textbf{(C) }2f(n)+1\qquad\textbf{(D) }f^2(n)\qquad \textbf{(E) }</math> |
| + | <math>\frac{1}{2}(f^2(n)-1)</math> | ||
Revision as of 16:50, 5 March 2014
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:
