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Difference between revisions of "1975 AHSME Problems/Problem 1"

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==Problem==
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The value of <math>\frac {1}{2 - \frac {1}{2 - \frac {1}{2 - \frac12}}}</math> is  
 
The value of <math>\frac {1}{2 - \frac {1}{2 - \frac {1}{2 - \frac12}}}</math> is  
  

Revision as of 15:43, 19 January 2021

Problem

The value of $\frac {1}{2 - \frac {1}{2 - \frac {1}{2 - \frac12}}}$ is

$\textbf{(A)}\ 3/4 \qquad \textbf{(B)}\ 4/5 \qquad \textbf{(C)}\ 5/6 \qquad \textbf{(D)}\ 6/7 \qquad \textbf{(E)}\ 6/5$


Solution

Solution by e_power_pi_times_i


Calculating, we find that $\frac {1}{2 - \frac {1}{2 - \frac {1}{2 - \frac12}}} = \frac {1}{2 - \frac {1}{2 - \frac {2}{3}}} = \frac {1}{2 - \frac {3}{4}} = \frac {1}{\frac {5}{4}} = \boxed{\textbf{(B) } \dfrac{4}{5}}$.

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