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Problems(1)

Find the floor

Source:

9/21/2010
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.
integrationfloor functioncalculusalgebraseries summationapproximationIMO Shortlist