Proof of lim n→∞(1+1/n)^n=e

prove that lim n→∞ (1+1/n)^n=e

let L=lim n → ∞ (1+1/n)^n

first find form of this limit

put n= ∞ 

(1+1/∞)^∞ 

(1+0)^∞ 

1^∞=1

Now we can using this rule,

L=e^lim n → ∞n(1+1/n -1)

L=e^lim x → ∞n(1/n) 

L=e^lim x → ∞ n/n

L=e^lim x → ∞ 1

L=e^1=e answer