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

We will start with $2+1=3$ and then apply the operation "invert and add one" three times. These iterations yield (after $3$ ): $\frac{4}{3}$ , $\frac{7}{4}$ , and finally $\boxed{\textbf{(B) } \frac{11}{7} }$

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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