Question

converges or diverges ?

Answer 1

\[\sum_{k=1}^{\infty}(\frac{ 3 }{ k! })\]

Answer 2

If\[\int\limits_{1}^{\infty}\frac{1}{x!}dx\]
diverges, then your series will diverge

Answer 3

your series will indeed diverge i worked it my self to see and it did

Answer 4

@henpen what is the theorem which you use?

Answer 5

If integral diverges, series diverges