{"status": "success", "data": {"description_md": "The sum\n$$\\frac{1}{2!}+\\frac{2}{3!}+\\frac{3}{4!}+\\cdots+\\frac{2021}{2022!}$$ can be expressed as $a-\\frac{1}{b!}$, where $a$ and $b$ are positive integers. What is $a+b$?\n\n$\\textbf{(A)}\\ 2020 \\qquad\\textbf{(B)}\\ 2021 \\qquad\\textbf{(C)}\\ 2022 \\qquad\\textbf{(D)}\\ 2023 \\qquad\\textbf{(E)}\\ 2024$", "description_html": "<p>The sum<br/>\n <span class=\"katex--display\">\\frac{1}{2!}+\\frac{2}{3!}+\\frac{3}{4!}+\\cdots+\\frac{2021}{2022!}</span>  can be expressed as  <span class=\"katex--inline\">a-\\frac{1}{b!}</span> , where  <span class=\"katex--inline\">a</span>  and  <span class=\"katex--inline\">b</span>  are positive integers. What is  <span class=\"katex--inline\">a+b</span> ?</p>\n<p> <span class=\"katex--inline\">\\textbf{(A)}\\ 2020 \\qquad\\textbf{(B)}\\ 2021 \\qquad\\textbf{(C)}\\ 2022 \\qquad\\textbf{(D)}\\ 2023 \\qquad\\textbf{(E)}\\ 2024</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": 1, "problem_name": "2022 AMC 10B Problem 9", "can_next": true, "can_prev": true, "nxt": "/problem/22_amc10B_p10", "prev": "/problem/22_amc10B_p08"}}