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2009 AMC 12A Problems/Problem 2

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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 ...

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}...

See Also

2009 AMC 12A (ProblemsResources)
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
2009 AMC 10A (ProblemsResources)
Preceded by
Problem 2
Followed by
Problem 4
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
Want to learn how to tackle those tough MATHCOUNTS and AMC counting and probability problems? Check out Art of Problem Solving's Introduction to Counting & Probability by David Patrick.
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