Question Number 104471 by Dwaipayan Shikari last updated on 21/Jul/20

Σ_(n=1) ^∞ ((e^n n!)/n^n )

Answered by MAB last updated on 21/Jul/20

let U_n =((n!)/n^n )e^n   by stirling formula: n!∽(√(2πn))((n/e))^n   we deduce: U_n ∽(√(2πn))  hence Σ_(n=1) ^∞ ((e^n n!)/n^n ) diverges