# Harmonic At It's Best

Calculus Level 4

Let

$\text{A}$ = $\frac{1}{1001} + \frac{1}{1002} + \frac{1}{1003} + \dots + \frac{1}{3001}$.

Then $x$ $\lt$ $\text{A}$ $\lt$ $\frac{y}{3}$.

Where $x$ is the greatest integer possible in its range and $y$ is the smallest integer possible in its range.

Find the value of $x + y$.

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