MathDB

21

Part of 2016 Harvard-MIT Mathematics Tournament

Problems(1)

2016 Guts #21

Source:

12/24/2016
Tim starts with a number nn, then repeatedly flips a fair coin. If it lands heads he subtracts 1 from his number and if it lands tails he subtracts 2. Let EnE_n be the expected number of flips Tim does before his number is zero or negative. Find the pair (a,b)(a,b) such that lim⁡n→∞(En−an−b)=0. \lim_{n \to \infty} (E_n-an-b) = 0.