Limit of ((1+1/n)^n-e)n as n approaches infinity

We know the limit of (1+1/n)^n goes to the Euler's number e as n goes to infinity. However, we need to be extra careful when we are evaluating the limit of n((1+1/n)^n-e) as n goes to infinity. This is a great L'Hospital's rule limit question to challenge calculus 1 and calculus 2 students. Check out my "100 calculus limits in one take":    • 100 calculus limits (ft epsilon-delta defi...   ---------------------------------------- 💪 Support this channel and get my math notes by becoming a patron:   / blackpenredpen   🛍 Shop my math t-shirt & hoodies: https://amzn.to/3qBeuw6 ---------------------------------------- #blackpenredpen #math #calculus #apcalculus #maths #calculus #blackpenredpen #mathforfun