Difference between revisions of "2009 AMC 12A Problems/Problem 2"

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{{duplicate|[[2009 AMC 12A Problems|2009 AMC 12A #2]] and [[2009 AMC 10A Problems|2009 AMC 10A #3]]}}
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== Problem ==
 
== Problem ==
 
Which of the following is equal to <math>1 + \frac {1}{1 + \frac {1}{1 + 1}}</math>?
 
Which of the following is equal to <math>1 + \frac {1}{1 + \frac {1}{1 + 1}}</math>?

Revision as of 05:06, 13 February 2009

The following problem is from both the 2009 AMC 12A #2 and 2009 AMC 10A #3, so both problems redirect to this page.

Problem

Which of the following is equal to $1 + \frac {1}{1 + \frac {1}{1 + 1}}$?

$\textbf{(A)}\ \frac {5}{4} \qquad \textbf{(B)}\ \frac {3}{2} \qquad \textbf{(C)}\ \frac {5}{3} \qquad \textbf{(D)}\ 2 \qquad \textbf{(E)}\ 3$

Solution

We compute:

\begin{align*} 1 + \frac {1}{1 + \frac {1}{1 + 1}} &= 1 + \frac {1}{1 + \frac {1}{1 + 1}} \\ &= 1 + \frac {1}{1 + \frac 12} \\ &= 1 + \frac {1}{\frac 32} \\ &= 1 + \frac 23 \\ &= \boxed{\frac 53} \end{align*}

See Also

2009 AMC 12A (ProblemsAnswer KeyResources)
Preceded by
Problem 1
Followed by
Problem 3
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
All AMC 12 Problems and Solutions