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

In this tutorial we shall discuss the very important formula of limits,

Let us consider the relation

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

Taking the limit as $x \to \infty$ for 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