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Source: Romanian selection test 1989, proposed by Gheorghe Eckstein

February 21, 2005
inductioninequalitieslimitalgebra proposedalgebra

Problem Statement

Prove that 1+2+…+n<2\sqrt {1+\sqrt {2+\ldots +\sqrt {n}}}<2, ∀n≥1\forall n\ge 1.
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