>>14368203>>14367994>>14368188Current term: (n/e)^n/n!
Next term: ((n+1)/e)^(n+1)/(n+1)!
Ratio of next over current: [(1+1/n)^n]/e
[(1+1/n)^n] goes to e
Ratio goes to 1, inconclusive.
>>14368005>>14368225Using Stirling's approximation of n!, n! is roughly sqrt(2n*pi)(n/e)^n.
So each term is roughly 1/sqrt(2n*pi), and this a scaled p-series (summation of 1/n^p) where p = 1/2. So the terms go to zero, but the series diverges to infinity.
