Revision as of 15:10, 21 April 2025 by Bot (Created page with "<div class="d-none"><math> \newcommand{\mathds}{\mathbb}</math></div> {{Alert-warning|This article was automatically generated from a tex file and may contain conversion errors. If permitted, you may login and edit this article to improve the conversion. }}Prove that <math>\sum_{n=0}^\infty\frac{1}{n!}=e</math>. Also, prove that <math>\left(1+\frac{x}{n}\right)^n\to e^x</math>, and that <math>\sum_{n=0}^\infty\frac{x^n}{n!}=e^x</math>, for <math>x=-1</math>, then for <...")
BBot
Apr 21'25
Exercise
[math]
\newcommand{\mathds}{\mathbb}[/math]
This article was automatically generated from a tex file and may contain conversion errors. If permitted, you may login and edit this article to improve the conversion.
Prove that [math]\sum_{n=0}^\infty\frac{1}{n!}=e[/math]. Also, prove that [math]\left(1+\frac{x}{n}\right)^n\to e^x[/math], and that [math]\sum_{n=0}^\infty\frac{x^n}{n!}=e^x[/math], for [math]x=-1[/math], then for [math]x\in\mathbb Z[/math], then for [math]x\in\mathbb R[/math].