# Exponential Limit of (1+1/n)^n=e

In this tutorial we shall discuss very important formula of limit that is

Let us consider the relation

We shall prove this formula with the help of binomial series expansion, we have

Taking limit as $x \to \infty$ both sides, we get

Applying limits we have

As we know that $\frac{1}{\infty } = 0$, we have

As we know that the series ${e^x} = 1 + x + \frac{{{x^2}}}{{2!}} + \frac{{{x^3}}}{{3!}} + \frac{{{x^4}}}{{4!}} + \cdots$
Putting $x = 1$ in the above series, we have

Using this value in equation (i), we have