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Algebra 1ChallengeRadicals

Radicals · Challenge problem

Rationalize each term, then evaluate the telescoping sum:

11+2+12+3+13+4+⋯+199+100.\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}}.