Question 174
A sequence $a_{0}, a_{1}, a_{2}, \ldots$ of real numbers is defined recursively by
$$
a_{0} = -1, \quad \sum_{k=0}^{n} \frac{a_{n-k}}{k+1} = 0 \quad \text{ for } n \geq 1.
$$
Prove that $a_{n} \gt 0$ for all $n \geq 1$.
$$
a_{0} = -1, \quad \sum_{k=0}^{n} \frac{a_{n-k}}{k+1} = 0 \quad \text{ for } n \geq 1.
$$
Prove that $a_{n} \gt 0$ for all $n \geq 1$.