Question 79
Let $n$ be an integer greater than $1$, and let $a_{0}, a_{1}, \ldots, a_{n}$ be real numbers with $a_{1} = a_{n-1} = 0$. Prove that for any real number $k$,
$$
\left|a_{0}\right| - \left|a_{n}\right| \leq \sum_{i=0}^{n-2} \left|a_{i} - k a_{i+1} - a_{i+2}\right|
$$
$$
\left|a_{0}\right| - \left|a_{n}\right| \leq \sum_{i=0}^{n-2} \left|a_{i} - k a_{i+1} - a_{i+2}\right|
$$