Question 72
Prove that
$$
1 - \frac{1}{2012} \left( \frac{1}{2} + \frac{1}{3} + \dots + \frac{1}{2013} \right) \gt \frac{1}{\sqrt[2012]{2013}}.
$$
$$
1 - \frac{1}{2012} \left( \frac{1}{2} + \frac{1}{3} + \dots + \frac{1}{2013} \right) \gt \frac{1}{\sqrt[2012]{2013}}.
$$