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Find the sum of $$\frac{1}{\sqrt{1}+ \sqrt{2}}+ \frac{1}{\sqrt{2}+ \sqrt{3}} + \text{and so on up to}+\frac{1}{ \sqrt {99}+ \sqrt{100}}.$$

What other similar sums lead to an exact whole number answer?

You don't need to have learned about summing series to do this problem!