Question 59
Let $(a_n)_{n \ge 0}$ be a sequence of positive real numbers such that
$$
\sum_{k=0}^{n} C_{n}^{k} a_{k} a_{n-k} = a_{n}^{2}, \text{ for any } n \ge 0.
$$
Prove that $(a_n)_{n \ge 0}$ is a geometrical sequence.
$$
\sum_{k=0}^{n} C_{n}^{k} a_{k} a_{n-k} = a_{n}^{2}, \text{ for any } n \ge 0.
$$
Prove that $(a_n)_{n \ge 0}$ is a geometrical sequence.