MathDB
2015 BMT Team 19

Source:

January 6, 2022
floor functionalgebra

Problem Statement

Two sequences (xn)n∈N(x_n)_{n\in N} and (yn)n∈N(y_n)_{n\in N} are defined recursively as follows:
x0=2015x_0 = 2015 and xn+1=⌊xn⋅yn+1yn−1⌋x_{n+1} =\left \lfloor x_n \cdot \frac{y_{n+1}}{y_{n-1}} \right \rfloor for all n≥0n \ge 0,
y0=307y_0 = 307 and yn+1=yn+1y_{n+1} = y_n + 1 for all n≥0n \ge 0.
Compute lim⁡n→∞xn(yn)2\lim_{n\to \infty} \frac{x_n}{(y_n)^2}.
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