{"status": "success", "data": {"description_md": "For all integers $n$ greater than $1$, define $a_n = \\frac{1}{\\log_n 2002}$. Let $b = a_2 + a_3 + a_4 + a_5$ and $c = a_{10} + a_{11} + a_{12} + a_{13} + a_{14}$. Then $b- c$ equals\n\n$\\mathrm{(A)}\\ -2\\qquad\\mathrm{(B)}\\ -1 \\qquad\\mathrm{(C)}\\ \\frac{1}{2002}\\qquad\\mathrm{(D)}\\ \\frac{1}{1001}\\qquad\\mathrm{(E)}\\ \\frac 12$\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>For all integers <span class=\"katex--inline\">n</span> greater than <span class=\"katex--inline\">1</span>, define <span class=\"katex--inline\">a_n = \\frac{1}{\\log_n 2002}</span>. Let <span class=\"katex--inline\">b = a_2 + a_3 + a_4 + a_5</span> and <span class=\"katex--inline\">c = a_{10} + a_{11} + a_{12} + a_{13} + a_{14}</span>. Then <span class=\"katex--inline\">b- c</span> equals</p>&#10;<p><span class=\"katex--inline\">\\mathrm{(A)}\\ -2\\qquad\\mathrm{(B)}\\ -1 \\qquad\\mathrm{(C)}\\ \\frac{1}{2002}\\qquad\\mathrm{(D)}\\ \\frac{1}{1001}\\qquad\\mathrm{(E)}\\ \\frac 12</span></p>&#10;<hr/>&#10;<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>&#10;", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 5, "problem_name": "2002 AMC 12B Problem 22", "can_next": true, "can_prev": true, "nxt": "/problem/02_amc12B_p23", "prev": "/problem/02_amc12B_p21"}}