Euler's number
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Euler's number (also known as Napier's constant), , is a mathematical constant, which is approximately equal to
It can be expressed as the limit, , and it can also be expressed as the infinite sum .
It is not be confused with (Euler-Mascheroni constant).
Proof of Equivalence of Definitions
Apply binomial expansion on the left hand side, we have:
Applications
Complex Numbers: