Is the sequence $\sqrt{1+\frac{1}{n^2}}$ increasing or decreasing? Is the sequence $\sqrt{1+\frac{1}{n^2}}$ increasing or decreasing?
I simplified it to $\frac{\sqrt{n^2+1}}{n}$, and I tried $a_{n+1}-a_n$ and $\frac{a_{n+1}}{a_n}$, but neither seem to work, how should I proceed?

$\sqrt{1+\frac{1}{n^2}} >  \sqrt{1+\frac{1}{(n+1)^2}}$ 
$\iff 1+\frac{1}{n^2} >  1+\frac{1}{(n+1)^2}$ 
$\iff \frac{1}{n^2} >  \frac{1}{(n+1)^2}$ 
$\iff {n^2} <  {(n+1)^2}$ 
$\iff {n^2} <  n^2+2n+1$
$\iff 0<  2n+1$
