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Subsequence that converges to sqrt(2)

Source: Putnam 1990 A2

July 12, 2013
Putnamcollege contests

Problem Statement

Is 2 \sqrt{2} the limit of a sequence of numbers of the form n3−m3 \sqrt[3]{n} - \sqrt[3]{m} , where n,m=0,1,2,⋯ n, m = 0, 1, 2, \cdots .
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