{"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$\\textbf{(A)}\\ \\frac{1+\\sqrt{5}}{2} \\qquad \\textbf{(B)}\\ 2 \\qquad \\textbf{(C)}\\ \\sqrt{5} \\qquad \\textbf{(D)}\\ 3 \\qquad \\textbf{(E)}\\ 4$", "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>\n<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>\n<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 10B Problem 16", "can_next": true, "can_prev": true, "nxt": "/problem/16_amc10B_p17", "prev": "/problem/16_amc10B_p15"}}