MathDB

19

Part of 2015 BMT Spring

Problems(2)

2015 BMT Team 19

Source:

1/6/2022
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}.
floor functionalgebra
BMT 2015 Spring - Individual 19

Source:

1/22/2022
It is known that 44 people A,B,CA, B, C, and DD each have a 1/31/3 probability of telling the truth. Suppose that ∙\bullet AA makes a statement. ∙\bullet BB makes a statement about the truthfulness of AA’s statement. ∙\bullet CC makes a statement about the truthfulness of BB’s statement. ∙\bullet DD says that CC says that BB says that AA was telling the truth. What is the probability that AA was actually telling the truth?
combinatorics