Radical Fractions, Man!

Algebra Level 3

The expression 112+21+123+32++1999910000+100009999 \frac {1}{ 1 \sqrt{2} + 2 \sqrt{1} }+ \frac {1}{ 2 \sqrt{3} + 3 \sqrt{2} } + \ldots + \frac {1} { 9999 \sqrt{10000} + 10000 \sqrt{9999} } is equal to ab \frac { a}{b} , where aa and bb are coprime positive integers. What is a+b a + b ?

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