Calculation of lim(1+1/n)^n

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lim+∞(1+1/n)n=e

Je sais que ça ne doit pas être sorcier, mais je me suis remis récemment à mes cours de DEUG 2ème année et je bloque (entre autres) sur ce résultat.
Il y a (au moins) deux réponses possibles, l'une ne va pas te plaire je crois.

1) Certains prennent ça comme définition de e, j'imagine que ce n'est pas ton cas sinon tu ne poserais pas la question...

2) Sinon, on écrit
(1+1/n)n=exp(nlog(1+1/n))=exp(n(1/n+o(1/n))=exp(1+o(1))→e.

J'ai utilisé comme prérequis log(1+u)=u+o(u).

Démonstration de l'inégalité : g inferieure ou égale à m

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