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Find the floor

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September 21, 2010
integrationfloor functioncalculusalgebraseries summationapproximationIMO Shortlist

Problem Statement

Find the integer represented by [∑n=1109n−2/3]\left[ \sum_{n=1}^{10^9} n^{-2/3} \right] . Here [x][x] denotes the greatest integer less than or equal to x.x.
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