MathDB
Putnam 2020 B6

Source: 81st William Lowell Putnam Competition

February 22, 2021
PutnamPutnam 2020

Problem Statement

Let nn be a positive integer. Prove that ∑k=1n(−1)⌊k(2−1)⌋≥0.\sum_{k=1}^n (-1)^{\lfloor k (\sqrt{2} - 1) \rfloor} \geq 0. (As usual, ⌊x⌋\lfloor x \rfloor denotes the greatest integer less than or equal to xx.)
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