Application of binomial theorem to simplify

Question

$a_n=\sqrt[n]{n}-1$

Use the binomial theorem to show that $n \ge \frac{n(n-1)}{2} a_n^2$

Please help with this problem - how do I apply the binomial theorem here? What do I choose for the k of n choose k?

Answer 1

Hint: Notice $(1+a_n)^n=n$. The second term in the expansion ($k=2)$ in LHS is $\frac{n(n-1)}{2}a_n^2$)