Question 47
Let $a_0, a_1, \dots, a_N$ be real numbers where $a_0 = a_N = 0$. Prove the inequality
$$ a_1^2 + a_2^2 + \dots + a_{N-1}^2 \le C \left((a_1 - a_0)^2 + (a_2 - a_1)^2 + \dots + (a_N - a_{N-1})^2\right), $$
where $C = \frac{N^2}{4}$.
$$ a_1^2 + a_2^2 + \dots + a_{N-1}^2 \le C \left((a_1 - a_0)^2 + (a_2 - a_1)^2 + \dots + (a_N - a_{N-1})^2\right), $$
where $C = \frac{N^2}{4}$.