Question 3
The sequence of real numbers $a_{0}, a_{1}, a_{2}, \ldots$ is defined recursively by
$$
a_{0}=-1, \quad \sum_{k=0}^{n} \frac{a_{n-k}}{k+1}=0 \quad \text{ for } \quad n \geq 1
$$
Show that $a_{n}\gt 0$ for $n \geq 1$.
$$
a_{0}=-1, \quad \sum_{k=0}^{n} \frac{a_{n-k}}{k+1}=0 \quad \text{ for } \quad n \geq 1
$$
Show that $a_{n}\gt 0$ for $n \geq 1$.