2018 AMC 10A Problems/Problem 1

Revision as of 20:01, 8 February 2018 by Welp... (talk | contribs) (Solution)

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)

-Welp...

See Also

2018 AMC 10A (ProblemsAnswer KeyResources)
Preceded by
First Problem
Followed by
Problem 2
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All AMC 10 Problems and Solutions

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