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MATH / The sequence {a_(n)} is defined by a₀=1,a₁=1, and a_(n)=a_(n−1)+(a_(n−1)²)/(a_(n−2)) for n≥2.The sequence {b_(n)} is defined by …

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problem

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}}.
Plain-text mathematical notation (without MathML)
The sequence {a_(n)} is defined by a₀=1,a₁=1, and a_(n)=a_(n−1)+(a_(n−1)²)/(a_(n−2)) for n≥2.The sequence {b_(n)} is defined by b₀=1,b₁=3, and b_(n)=b_(n−1)+(b_(n−1)²)/(b_(n−2)) for n≥2.Find (b₃₂)/(a₃₂).
Original LaTeX notation
The sequence $\{a_n\}$ is defined by $$
a_0 = 1,a_1 = 1, \text{ and } a_n = a_{n - 1} + \frac {a_{n - 1}^2}{a_{n - 2}}\text{ for }n\ge2.
$$The sequence $\{b_n\}$ is defined by $$
b_0 = 1,b_1 = 3, \text{ and } b_n = b_{n - 1} + \frac {b_{n - 1}^2}{b_{n - 2}}\text{ for }n\ge2.$$Find $\frac {b_{32}}{a_{32}}$.

level

Level 4

type

Intermediate Algebra

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task_id
950f94fb-174a-5910-bcfa-e5c948858194
task_key
intermediate~5falgebra--test--950f94fb-174a-5910-bcfa-e5c948858194
task_revision_id
1
config / split
intermediate_algebra / test

Official source

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