Difference between revisions of "1964 AHSME Problems/Problem 31"
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<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>\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> | <math>\frac{1}{2}(f^2(n)-1)</math> | ||
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| + | ==See Also== | ||
| + | {{AHSME 40p box|year=1964|num-b=30|num-a=32}} | ||
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| + | [[Category:Introductory Algebra Problems]] | ||
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| + | {{MAA Notice}} | ||
Revision as of 22:15, 24 July 2019
Problem
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:
See Also
| 1964 AHSC (Problems • Answer Key • Resources) | ||
| Preceded by Problem 30 |
Followed by Problem 32 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 • 26 • 27 • 28 • 29 • 30 • 31 • 32 • 33 • 34 • 35 • 36 • 37 • 38 • 39 • 40 | ||
| All AHSME Problems and Solutions | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
