1. ## Inequality

Hey

For A Sequence
$a_n=n^{\frac{1}{n}}-1$
Where $a_n>0,n>1$

How Can I Deduce That
$\forall n>1,n-1\geq\frac{1}{2}n\left(n-1\right)a_n^2$

2. Rearrange as $n=(1+a_n)^n$ and binomial expansion $n=1+na_n+\frac{n(n-1)}2a_n^2+\dots>1+\frac{n(n-1)}2a_n^2$ does the trick.