# 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 for both sides, we get

Applying limits we have

As we know that , we have

As we know that the series ,

putting in the above series, we have

Using this value in equation (i), we have

Qin

August 15@ 2:32 pmHi:

I have a further question that how to prove e=1+x+x^2/2!+... without using taylor expansion.Because I think taylor expansion is based on derivative of e^x. And in order to derive the derivative of e^x, we may need a lot of some other derivatives or limits which finally resorts to lim(1+1'x)^x=e . And they cause a proof loop.so we may find a another approach to e's proof