4

Part of 1963 Polish MO Finals

Problems(1)

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

Source: Polish MO Finals 1963 p4

Prove that for every natural number

n

the inequality holds

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

algebrainequalities