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2016 AMC 10B Problems/Problem 16

Revision as of 08:23, 21 February 2016 by Mathlogin (talk | contribs) (Created page with "==Problem== The sum of an infinite geometric series is a positive number <math>S</math>, and the second term in the series is <math>1</math>. What is the smallest possible va...")
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Problem

The sum of an infinite geometric series is a positive number $S$, and the second term in the series is $1$. What is the smallest possible value of $S?$

$\textbf{(A)}\ \frac{1+\sqrt{5}}{2} \qquad \textbf{(B)}\ 2 \qquad \textbf{(C)}\ \sqrt{5} \qquad \textbf{(D)}\ 3 \qquad \textbf{(E)}\ 4$

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