Just a simple question, I'm using the series 1 + 1/1! + 1/2! + 1/3! ... + 1/n! to compute e, the first 3 terms: 1, 1/1!, 1/2! come out as 1, 1, 0.5, but it seems all the other terms contain recurring decimals, like 1/3! = 1/6 = 0.166666.....
I was wondering if there were any terms after n=2 for 1/n! where the result does not come out as a recurring decimal, I thought it's likely there isn't, but is there a proof?