Mathematica 7 gives an answer, Mathematica 10 does not?

Questions
1

Clear[a, n, r]
a[n_] = Sin[Pi*n/2]/n!
Table[a[n], {n, 0, 10}]
r = Limit[Abs[a[n]]^(1/n), n → Infinity]

What do I need to change to make MMA10.3 (OSX) give me an answer? Thanks for suggestions.

Gary Bollenbach

2

The following works in Mma 10.4:

Limit[Simplify[(Abs[Sin[Pi*n/2]]/n!)^(1/n) // TrigToExp, 
  Element[n, Integers]], n -> Infinity, 
 Assumptions -> Element[n, Integers]]
3

Thanks, that’s what I needed.