A Floor-Sqrt Recurrence Limit

★ 8/10Limits calculus sequences Estimation Induction

Problem

A sequence $\{x_n\}$ satisfies $x_1=1$ and $x_{n+1}=x_n+\lfloor\sqrt{x_n}\rfloor$ . Find

\lim_{n\to+\infty}\frac{x_n}{n^2}.

Answer

Solution

Difficulty	8/10
Topics	Limits, calculus, sequences, Estimation, Induction

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