I want to study the convergence of the series of general term $sin(\pi en!)$ In my naive way I see that this limit does not exist at infinity since e is an irrational number but they say it's zero Any explanation to this???? Thanks in advance
I didn't know how to solve this problem.  How to prove $$\sum_{n=0}^{\infty}\sin(e\pi n!)$$ converges?
Following the guidelines suggested in , I am going to post a proposed proof as an answer to the theorem below. I believe the proof works, but would appreciate any needed corrections.  Theorem If a series $\sum_{n=1}^{\infty}a_n$ of real numbers converges then $\lim_{n \to \infty}a_n = 0$