2018 AMC 10A Problems/Problem 1

Problem

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

$2+1=3$ , so the reciprocal is $\frac{1}{3}$ . Summing $1$ and repeating leads to $\frac{3}{4}$ . Rinse and repeat to get $\frac{4}{7}$ . Adding $1$ to that is $\frac{11}{7}$ (B)

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2018 AMC 10A (Problems • Answer Key • Resources)
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All AMC 10 Problems and Solutions

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2018 AMC 10A Problems/Problem 1

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