# What is the limit of #(1+1/x)^x# as x approaches infinity?

##### 1 Answer

#### Explanation:

We are trying to find:

Let's begin by expanding the term in brackets using the binomial theorem

such that the

We can simplify this expression by cancelling terms with

From this we can see that the term on the right goes to 1 as

This is the known series for the natural number,

Interestingly, this limit sometimes used to define

https://en.wikipedia.org/wiki/Binomial_theorem