2009 AMC 12A Problem 2

Starting inside, $1 + 1 = 2,$ so $1 + \dfrac{1}{2} = \dfrac{3}{2}.$ Then $\dfrac{1}{\frac{3}{2}} = \dfrac{2}{3},$ and $1 + \dfrac{2}{3} = \dfrac{5}{3}.$ Thus, the correct answer is C.