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This is actually quite easy to prove. The Taylor series of the exponential function, e^x (using "^" for power) is 1 + x^1/1! + x^2/2! + x^3/3! + x^4/4! ..., so all you need to do is replace the exponent "x" by 1.

(To be precise, you would also have to prove that the corresponding Taylor series is correct - that means proving that the residual tends towards zero. This is the case for most commonly used functions, but it must still be proven for individual cases such as this one.)

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Q: How can you Prove that e equals the infinite sum of 1 divided by x factorial?
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