I have to prove that $e$ is irrational using this inequality
The exercise leave the hint "prove by contradiction". I know too that $2<e\le 3$.
What I tried is set $e=p/q$ for $p,q\in\Bbb N$, and $\sum 1/k!=A/n!$ where $A\in\Bbb N$. Then I written
but I dont get any idea from here. Indeed I dont know exactly what to do here, I never used a inequality to prove the irrationality of a number. Can you give me some hint (or solution)? Thank you.
P.S.: I dont know exactly what kind of tags I have to use for this question.