MathDB
Sum with floor function and square roots

Source: Czech and Slovak Olympiad 1973, National Round, Problem 4

July 16, 2024
algebrafloor functionSumsum of rootsfunction

Problem Statement

For any integer n≥2n\ge2 evaluate the sum ∑k=1n2−1⌊k⌋.\sum_{k=1}^{n^2-1}\bigl\lfloor\sqrt k\bigr\rfloor.
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