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Two Sequences

Source: AIME 2008II Problem 6

April 3, 2008
LaTeXinductionratiofactorialUSAMTSAMC

Problem Statement

The sequence {an} \{a_n\} is defined by a_0 \equal{} 1,a_1 \equal{} 1, \text{ and } a_n \equal{} a_{n \minus{} 1} \plus{} \frac {a_{n \minus{} 1}^2}{a_{n \minus{} 2}}\text{ for }n\ge2. The sequence {bn} \{b_n\} is defined by b_0 \equal{} 1,b_1 \equal{} 3, \text{ and } b_n \equal{} b_{n \minus{} 1} \plus{} \frac {b_{n \minus{} 1}^2}{b_{n \minus{} 2}}\text{ for }n\ge2. Find b32a32 \frac {b_{32}}{a_{32}}.
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