{"status": "success", "data": {"description_md": "Let $S: \\mathbb{Z^+} \\rightarrow \\mathbb{Z^+}$ be a function such that:\n    $$S(x) = \\sum\\limits_{n = 1}^{60}{n(1 + x)^n} $$\n\nIf $60^2\\cdot S(60) = a(b^b) + b$, where $b$ is maximized and $a, b \\in \\mathbb{Z^+}$, find $\\left\\lfloor\\dfrac{a + b}{10}\\right\\rfloor$.    ", "description_html": "<p>Let <span class=\"katex--inline\">S: \\mathbb{Z^+} \\rightarrow \\mathbb{Z^+}</span> be a function such that:<br/>&#10;<span class=\"katex--display\">S(x) = \\sum\\limits_{n = 1}^{60}{n(1 + x)^n}</span></p>&#10;<p>If <span class=\"katex--inline\">60^2\\cdot S(60) = a(b^b) + b</span>, where <span class=\"katex--inline\">b</span> is maximized and <span class=\"katex--inline\">a, b \\in \\mathbb{Z^+}</span>, find <span class=\"katex--inline\">\\left\\lfloor\\dfrac{a + b}{10}\\right\\rfloor</span>.</p>&#10;", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 4, "problem_name": "TxO Math Bowl 2024 - Individuals B - Problem 8", "can_next": true, "can_prev": true, "nxt": "/problem/txo2024indivsB-p09", "prev": "/problem/txo2024indivsB-p07"}}