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1 +1/\sqrt{2} + 1/\sqrt{3} + ... +1/ {\sqrt{n}} > \sqrt{n-1}.

Source: Polish MO Finals 1963 p4

August 30, 2024
algebrainequalities

Problem Statement

Prove that for every natural number n n the inequality holds 1+12+13+…+1n>n−1. 1 + \frac{1}{\sqrt{2}} + \frac{1}{\sqrt{3}} + \ldots + \frac{1}{\sqrt{n}} > \sqrt{n-1}.
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