A Sum with Fractions and Roots

Algebra Level 2

Determine the sum \[ \frac{1}{\sqrt{1}+\sqrt{2}} + \frac{1}{\sqrt{2}+\sqrt{3}} + \frac{1}{\sqrt{3}+\sqrt{4}} + \cdots + \frac{1}{\sqrt{99} + \sqrt{100} }.\]

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