Harmonic At It's Best

Calculus Level 4

Let

A\text{A} = 11001+11002+11003++13001\frac{1}{1001} + \frac{1}{1002} + \frac{1}{1003} + \dots + \frac{1}{3001}.

Then xx <\lt A\text{A} <\lt y3\frac{y}{3}.

Where xx is the greatest integer possible in its range and yy is the smallest integer possible in its range.

Find the value of x+y x + y .

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