Prove-that-lim-n-1-n-1-n-e-

Question Number 8839 by tawakalitu last updated on 31/Oct/16

Prove that .

\lim_{n \to \infty} {(1 + n)}^{1 / n} = e

Answered by FilupSmith last updated on 31/Oct/16

L = \lim_{n \to \infty} {(1 + n)}^{1 / n}

L = \lim_{n \to \infty} \exp {\frac{1}{n} \ln (1 + n)}

L = \exp {\lim_{n \to \infty} \frac{1}{n} \ln (1 + n)}

L^{'} Hopitals law

L = \exp {\lim_{n \to \infty} \frac{1}{n + 1}}

L = e^{0}

L = 1

\lim_{n \to \infty} {(1 + n)}^{1 / n} = 1

\lim_{n \to \infty} {(1 + n)}^{1 / n} \neq e

Commented by tawakalitu last updated on 31/Oct/16

I really appreciate sir .