Tuesday, 28 May 2019

real analysis - Prove that $1 + frac{1}{sqrt{2}} + frac{1}{sqrt{3}} + ... + frac{1}{sqrt{n}}geq sqrt{n}$

Anyone who can solve it or give me an idea on how to try to do it myself?




$$1 + \frac{1}{\sqrt{2}} + \frac{1}{\sqrt{3}} + ... + \frac{1}{\sqrt{n}}\geq \sqrt{n}, \;\;\;n \in \mathbb{N^*}$$

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