Question 60
Let $(a_n)_{n \ge 1}$ be a sequence of real positive numbers, such that the sequence $(a_{n+1} - a_n)_{n \ge 1}$ converges to a non-zero limit. Compute the limit
$$
\lim_{n \to \infty} \left( \frac{a_{n+1}}{a_n} \right)^n .
$$
$$
\lim_{n \to \infty} \left( \frac{a_{n+1}}{a_n} \right)^n .
$$