HMMT 2020 U33

Estimate

$N=\prod_{n=1}^{\infty} n^{n^{-1.25}}$

An estimate of $E>0$ will receive $\lfloor 22 \min (N / E, E / N)\rfloor$ points.

Dataset text NuminaMath olympiads. 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.