olymmath

AIME 2008b Problem 6

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The sequence {an}\{a_n\} is defined by a0=1,a1=1, and an=an−1+an−12an−2 for n≥2.a_0 = 1,a_1 = 1, \text{ and } a_n = a_{n - 1} + \frac {a_{n - 1}^2}{a_{n - 2}}\text{ for }n\ge2. The sequence {bn}\{b_n\} is defined by b0=1,b1=3, and bn=bn−1+bn−12bn−2 for n≥2.b_0 = 1,b_1 = 3, \text{ and } b_n = b_{n - 1} + \frac {b_{n - 1}^2}{b_{n - 2}}\text{ for }n\ge2. Find b32a32\frac {b_{32}}{a_{32}}.

Dataset text AIME 1983 to 2026. Quoted with source.

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