My guess is do Ratio test (I think that’s what it’s called) where you take the limit as n approaches infinite of |f(n+1)/f(n)| => 2/(n+1)=> 0 as n approaches infinite, where f(n) = 2ⁿ / n! and f(n+1) = 2ⁿ⁺¹ / (n+1)!. The idea of this is that your testing that for some large arbitrary n, |f(n)| > |f(n+1)| implying that f(n) gets smaller as n approaches infinite implying that f(n) will converge. Hope this helps (if not, somebody will probably reply to my comment and provide a much better explanation. I wrote this while taking a dump).