Use of Hôpital's rules to calculate also the sequences Hoping that my question is clear, I would like to understand because the L'Hôpital's rules are used in several questions on Math.SE (an answer for example) to calculate the sequences,
$$(a_n)_{n\in\Bbb N}, \quad \text {or} \quad \{a_n\}, \quad n\in\Bbb N$$
During my university period I had been instructed that Hôpital's theorems cannot be applied.

The analog of L'Hospital rule for sequences is the Stolz-Cesaro theorem:
https://www.google.com/url?sa=t&rct=j&q=&esrc=s&source=web&cd=&cad=rja&uact=8&ved=2ahUKEwjAvLyEgYnrAhUlJTQIHayoC_YQFjAAegQIAxAB&url=https%3A%2F%2Fen.wikipedia.org%2Fwiki%2FStolz%25E2%2580%2593Ces%25C3%25A0ro_theorem&usg=AOvVaw1iQkM4oA1MZoySX8fqNTXe
