I'm looking for proofs to the 2 following results.(adsbygoogle = window.adsbygoogle || []).push({});

Let

[tex] \displaystyle{e=: \lim_{n\rightarrow +\infty} \left(1+\frac{1}{n}\right)^n} [/tex]

Show that:

1. Universality of e.

[tex] \sum_{k=0}^{\infty} \frac{1}{k!} = e [/tex]

2. Derivative of [itex]e^x [/itex].

[tex] (e^x)' = e^x, ~ \forall x\in\mathbb{R} [/tex]

Searching google didn't get me satisfactory results.

Could you, please, post or link to proofs ? Thank you!

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