Prove that:

(1 + x/n)^n = e^x as n approaches infinity

Without using l'Hopitals Rule?

The book proves (1 + 1/n)^n = e as n tends to infinity.

by considering f(x) = ln(x) and f'(x) = 1/x and f'(1) = 1

Then from first principles proves eventually that (1 + 1/n)^n = e as n tends to infinity, by letting n = 1/h etc.