2009 AMC 10A Problem 3

Problem 3 of 25EasierAlgebra

Which of the following is equal to

1 + \cfrac{1}{1 + \cfrac{1}{1 + 1}}?

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Solution

Working outward,

\begin{aligned} &1 + \cfrac{1}{1 + \cfrac{1}{1 + 1}} \\ &= 1 + \cfrac{1}{1 + \dfrac{1}{2}} \\ &= 1 + \dfrac{1}{\frac{3}{2}} \\ &= 1 + \dfrac{2}{3} = \dfrac{5}{3}. \end{aligned}

Thus, the correct answer is C.

Concepts: continued fraction · fraction

Problem text and solution from the LIVE past-contest archive. See also the AoPS wiki page for community solutions.