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>,...") |
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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 17:50, 5 March 2014
Let
Then , expressed in terms of
, equals: