Square roots galore

Algebra Level 2

Evaluate the following sum:

11×2+2×1+12×3+3×2+...+19999×10000+10000×9999. \frac{1}{ \sqrt1 \times 2+\sqrt2 \times 1} + \frac{1}{ \sqrt2 \times 3+\sqrt3 \times 2}+ ...+\frac{1}{ \sqrt{9999} \times 10000+\sqrt{10000} \times 9999}.

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