VTRMC 2013 Problem 3

Define a sequence $(a_n)$ for $n\ge1$ by $a_1=2$ and $a_{n+1}=a_n^{1+n^{-3/2}}$ . Is $(a_n)$ convergent (i.e. $\lim_{n\to\infty}a_n<\infty$ )?

Dataset text AI-MO AoPS. Quoted with source.

Solutions

No solution is on olymmath yet. Official and human solutions come first when they arrive. AI solutions come after them, with a label.