Difference between revisions of "University of South Carolina High School Math Contest/1993 Exam/Problem 24"
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== Solution == | == Solution == | ||
Notice that for each <math>f_{n}(3)</math> where <math>n</math> is odd, the value is <math>1/5</math> and for each value of <math>f_{n}(3)</math> where <math>n</math> is even, the value is <math>3</math>. It follows that the answer is <math>1/5</math>. | Notice that for each <math>f_{n}(3)</math> where <math>n</math> is odd, the value is <math>1/5</math> and for each value of <math>f_{n}(3)</math> where <math>n</math> is even, the value is <math>3</math>. It follows that the answer is <math>1/5</math>. | ||
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Revision as of 17:21, 17 August 2006
Problem
If and in general
then
![$\mathrm{(A) \ }3 \qquad \mathrm{(B) \ }1993 \qquad \mathrm{(C) \ }\frac 12 \qquad \mathrm{(D) \ }\frac 15 \qquad \mathrm{(E) \ } -2^{-1993}$](http://latex.artofproblemsolving.com/0/5/e/05e4773b2648f5283a450bb27e1fcda8639e663c.png)
Solution
Notice that for each where
is odd, the value is
and for each value of
where
is even, the value is
. It follows that the answer is
.
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