479.The Frog's Favorite Number
★★★random walksCh. 2 — Axiomatic and Conditional Probability444+ Problems in Probability
A frog starts at 0 and repeatedly jumps forward 1 or 2 steps, each with probability . Let be the probability the frog ever lands on position . Find the largest value of .
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Condition on the first jump to get a two-term recursion, and compute the first few values before assuming monotonicity.
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