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SMO 2018 Open Round 1 Question 10

SMO · SMO 2018 Open Round 1

Question 10

Find the smallest integer r such that $$1+\frac 1{\sqrt 2}+\frac 1{\sqrt 3}+\frac 1{\sqrt 4}+\cdots+\frac 1{\sqrt{2018}}\le r\sqrt{2018}.$$