# How do you calculate Euler's Number?

We can compute an approximating fraction by truncating the series as we see fit. For example, If we restrict ourself to the first five terms, we get:

And for further comparison, if we take further terms we get:

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The Euler-Mascheroni constant is defined as:

Then:

So:

and:

As the series:

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Euler's number, denoted as ( e ), is calculated using the following infinite series:

[ e = 1 + \frac{1}{1!} + \frac{1}{2!} + \frac{1}{3!} + \frac{1}{4!} + \frac{1}{5!} + \cdots ]

Alternatively, it can be calculated using the limit of the expression ( \left(1 + \frac{1}{n}\right)^n ) as ( n ) approaches infinity.

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