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I'm looking for proofs to the 2 following results.
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!
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!