{"status": "success", "data": {"description_md": "An infinite geometric series has sum $2005$. A new series, obtained by squaring each term of the original series, has $10$ times the sum of the original series. The common ratio of the original series is $\\frac{m}{n}$ where $m$ and $n$ are relatively prime integers. Find $m+n$.\n___\nLeading zeroes must be inputted, so if your answer is `34`, then input `034`. Full 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>An infinite geometric series has sum <span class=\"katex--inline\">2005</span>. A new series, obtained by squaring each term of the original series, has <span class=\"katex--inline\">10</span> times the sum of the original series. The common ratio of the original series is <span class=\"katex--inline\">\\frac{m}{n}</span> where <span class=\"katex--inline\">m</span> and <span class=\"katex--inline\">n</span> are relatively prime integers. Find <span class=\"katex--inline\">m+n</span>.</p>&#10;<hr><p>Leading zeroes must be inputted, so if your answer is <code>34</code>, then input <code>034</code>. 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": "2005 AIME II Problem 3", "can_next": true, "can_prev": true, "nxt": "/problem/05_aime_II_p04", "prev": "/problem/05_aime_II_p02"}}