2018 AMC 10A Problems/Problem 1

What is the value of $\left(\left((2+1)^{-1}+1\right)^{-1}+1\right)^{-1}+1?$ $\textbf{(A) } \frac58 \qquad \textbf{(B) }\frac{11}7 \qquad \textbf{(C) } \frac85 \qquad \textbf{(D) } \frac{18}{11} \qquad \textbf{(E) } \frac{15}8$

Solution

Evaluating the expressions starting with the innermost one, we get that the answer is $\boxed{\textbf{(B)}\ \frac{11}{7}}$ {MAA Notice}

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2018 AMC 10A Problems/Problem 1

Solution