List of representations of e: Difference between revisions

→‎As the limit of a sequence: Added factorial/derangement definition.
(→‎As an infinite series: minor simplification: 3 - \sum_{k=2}^\infty \frac{1}{k! (k-1) k})
(→‎As the limit of a sequence: Added factorial/derangement definition.)
 
:<math>e= \lim_{n \to \infty}\left (1+ \frac{1}{n} \right )^n.</math>
 
The ratio of the [[factorial]] <math>n!</math>, that counts all [[permutation|permutations]] of an orderet set S with [[cardinality]] <math>n</math>, and the [[derangement]] function <math>!n</math>, which counts the amount of permutations where no element appears in its original position, tends to <math>e</math> as <math>n</math> grows.
 
:<math>e= \lim_{n \to \infty} \frac{n!}{!n}.</math>
 
== In trigonometry ==
22

edits