
Originally Posted by
firebio
Proof by induction that
$\displaystyle
1+ \frac{1}{\sqrt{2}}+\frac{1}{\sqrt{3}}+...+\frac{1} {\sqrt{n}}< 2\sqrt{n}
$
K+1 Step
$\displaystyle
1+ \frac{1}{\sqrt{2}}+\frac{1}{\sqrt{3}}+...+\frac{1} {\sqrt{k}}+\frac{1}{\sqrt{k+1}}< 2\sqrt{k}+\frac{1}{\sqrt{k+1}}
$
$\displaystyle
1+ \frac{1}{\sqrt{2}}+\frac{1}{\sqrt{3}}+...+\frac{1} {\sqrt{k}}+\frac{1}{\sqrt{k+1}}<\frac{2\sqrt{k} \sqrt{k+1}}{\sqrt{k+1}}
$
Then im stuck here....
Any help would be appreciated.
Thanks in advance