What is \frac{1}{\sqrt{10}+\sqrt{9}} + \frac{1}{\sqrt{11}+\sqrt{10}} + \frac{1}{\sqrt{12}+\sqrt{11}} + ... + \frac{1}{\sqrt{196}+\sqrt{195}} equal to?

Explanation

Rationalizing each term by multiplying the numerator and denominator by their conjugates gives (\sqrt{10}-\sqrt{9}) + (\sqrt{11}-\sqrt{10}) + ... + (\sqrt{196}-\sqrt{195}). This is a telescoping series where intermediate terms cancel out, leaving \sqrt{196} - \sqrt{9} = 14 - 3 = 11.

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