{"status": "success", "data": {"description_md": "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 $S?$\n\n$\\textbf{(A)}\\ \\frac{1+\\sqrt{5}}{2} \\qquad<br>\\textbf{(B)}\\ 2 \\qquad<br>\\textbf{(C)}\\ \\sqrt{5} \\qquad<br>\\textbf{(D)}\\ 3 \\qquad<br>\\textbf{(E)}\\ 4$\n___\nFull credit goes to [MAA](https://maa.org/) for authoring these problems. These problems were taken on the [AOPS](https://artofproblemsolving.com/) website.", "description_html": "<p>The sum of an infinite geometric series is a positive number  <span class=\"katex--inline\">S</span> , and the second term in the series is  <span class=\"katex--inline\">1</span> . What is the smallest possible value of  <span class=\"katex--inline\">S?</span> </p>&#10;<p> <span class=\"katex--inline\">\\textbf{(A)}\\ \\frac{1+\\sqrt{5}}{2} \\qquad\\textbf{(B)}\\ 2 \\qquad\\textbf{(C)}\\ \\sqrt{5} \\qquad\\textbf{(D)}\\ 3 \\qquad\\textbf{(E)}\\ 4</span> </p>&#10;<hr><p>Full credit goes to <a href=\"https://maa.org/\">MAA</a> for authoring these problems. These problems were taken on the <a href=\"https://artofproblemsolving.com/\">AOPS</a> website.</p>", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 3, "problem_name": "2016 AMC 12B Problem 14", "can_next": true, "can_prev": true, "nxt": "/problem/16_amc12B_p15", "prev": "/problem/16_amc12B_p13"}}