Nearest Integer Reciprocals

★ 7/10number theory Counting sequences Estimation

Problem

Let $f(n)$ be the integer nearest to $\sqrt{n}$ . If

\frac{1}{f(1)} + \frac{1}{f(2)} + \cdots + \frac{1}{f(m)} = 4034,

find the positive integer $m$ .

Answer

Solution

Difficulty	7/10
Topics	number theory, Counting, sequences, Estimation

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