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Raskolnikov is right: you can't prove a definition. You can prove, however, that this is a good definition, i.e. that the limit exists, and is finite.

Feb 9, 2018 · Proof of e as a limit Ask Question Asked 7 years, 8 months ago Modified 7 years, 8 months ago

Are you familiar with Taylor series? Series solutions of differential equations at regular points? From what foundation/background are you approaching this problem?

Oct 28, 2014 · e as sum of an infinite series [duplicate] Ask Question Asked 11 years ago Modified 10 years, 9 months ago

Jul 19, 2016 · I want to understand something about the derivation of $\\text{Var}(X) = E[X^2] - (E[X])^2$ Variance is defined as the expected squared difference between a random variable …

Apr 12, 2013 · Now $e (0)=e' (0)=1$ implies that the tangent line to $e (t)$ at $0$ is $t \mapsto 1+t$, and so for sufficiently small $t$ we should have $e (t)\simeq 1+t$, which this …

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Jul 15, 2016 · The limit definition of $e$ gives the best intuition toward how $e$ can model continuous growth. $$\lim\limits_ {n \to \infty} \left ( 1 + \frac1n\right)^n$$ Let n represent n …

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