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IL-GILLIS 2011 Problem 2

    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}} .

    Dataset text AI-MO AoPS. Quoted with source.

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