As A Continued Fraction
Euler proved that the number e is represented as the infinite simple continued fraction (sequence A003417 in OEIS):
Its convergence can be tripled by allowing just one fractional number:
Here are some infinite generalized continued fraction expansions of e. The second is generated from the first by a simple equivalence transformation.
This last, equivalent to, is a special case of a general formula for the exponential function:
Read more about this topic: List Of Representations Of E
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