800 Followers Problem #2

Algebra Level 4

The sequence \(\{a_n\}\) is defined by \[a_0 = 1,a_1 = 1, \text{ and } a_n = a_{n - 1} + \dfrac {a_{n - 1}^2}{a_{n - 2}}\text{ for }n\ge2.\] The sequence \(\{b_n\}\)is defined by \[b_0 = 1,b_1 = 3, \text{ and } b_n = b_{n - 1} + \dfrac {b_{n - 1}^2}{b_{n - 2}}\text{ for }n\ge2.\]

Find \(\dfrac {b_{32}}{a_{32}}\).

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