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Israel 2011 Q2 - Evaluate sum of roots

Source: Israel National Olympiad 2011 Q2

August 8, 2019
algebrarootspolynomialsum of roots

Problem Statement

Evaluate the sum 1−12⋅1⋅3+2−12⋅3⋅5+3−12⋅5⋅7+⋯+40−12⋅79⋅81\sqrt{1-\frac{1}{2}\cdot\sqrt{1\cdot3}}+\sqrt{2-\frac{1}{2}\cdot\sqrt{3\cdot5}}+\sqrt{3-\frac{1}{2}\cdot\sqrt{5\cdot7}}+\dots+\sqrt{40-\frac{1}{2}\cdot\sqrt{79\cdot81}}.
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