DE-MO 2004 Problem 4

For a positive integer $n,$ let $a_n$ be the integer closest to $\sqrt{n}.$ Compute $\frac{1}{a_1 } + \frac{1}{a_2 }+ \cdots + \frac{1}{a_{2004}}.$

Dataset text AI-MO AoPS. Quoted with source.

Solutions

No solution is on olymmath yet. Official and human solutions come first when they arrive. AI solutions come after them, with a label.