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Answers for “为什么证明 $-\frac{2}{3}a_n+\frac{1}{3}\le0$ 归结为已知的界 $a_n\ge\frac{1}{2}$?”

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Subtract ana_n from both sides of the recurrence relation. Distribute the 13\frac{1}{3} and combine like terms to simplify the expression to −23an+13-\frac{2}{3}a_n + \frac{1}{3}.

Conditions: The recurrence relation is an+1=13(an+1)a_{n+1}=\frac{1}{3}(a_n+1).; The goal is to analyze the sign of the difference to determine monotonicity.