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Classic Discriminant Trick

Source: AMC 10B 2016 #16

February 21, 2016
AMCAMC 10AMC 10 B2015 AMC 8geometric series

Problem Statement

The sum of an infinite geometric series is a positive number SS, and the second term in the series is 11. What is the smallest possible value of S?S?
<spanclass=′latex−bold′>(A)</span> 1+52<spanclass=′latex−bold′>(B)</span> 2<spanclass=′latex−bold′>(C)</span> 5<spanclass=′latex−bold′>(D)</span> 3<spanclass=′latex−bold′>(E)</span> 4<span class='latex-bold'>(A)</span>\ \frac{1+\sqrt{5}}{2} \qquad <span class='latex-bold'>(B)</span>\ 2 \qquad <span class='latex-bold'>(C)</span>\ \sqrt{5} \qquad <span class='latex-bold'>(D)</span>\ 3 \qquad <span class='latex-bold'>(E)</span>\ 4
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