AT-OEMO-REG 2005 Problem 1

Show for all integers $n \ge 2005$ the following chaine of inequalities: $(n+830)^{2005}<n(n+1)\dots(n+2004)<(n+1002)^{2005}$

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.