Prove that for every positive integer n,

Chapter 5, Problem 27E

(choose chapter or problem)

Prove that for every positive integer $n$,

$1+\frac{1}{\sqrt{2}}+\frac{1}{\sqrt{3}}+\cdots+\frac{1}{\sqrt{n}}>2(\sqrt{n+1}-1) \text {. }$

Equation Transcription:

$n$

$1\ +\ \frac{1}{\sqrt{2}}\ +\ \frac{1}{\sqrt{3}}\ +\ \cdot{}\cdot{}\cdot{}\ +\ \frac{1}{\sqrt{n}}\ >\ 2(\sqrt{n\ +\ 1}\ -1)$

Text Transcription:

1+\frac{1}{\sqrt{2}}+\frac{1}{\sqrt{3}}+\cdots+\frac{1}{\sqrt{n}}>2(\sqrt{n+1}-1)

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