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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