Question

Question #ec63c

Answer 1

The limit does not exist, it diverges, and oscillates between `+-oo`

Explanation:

We seek:

`L = lim_(n rarr oo) nsin(2pie n!)`

We could probably form a formal proof using Stirling's approximation formula.

But we can form a intuitive solution by firstly noting that `-1 le sin alpha le 1`, and `Asin alpha` will oscillate between `+-A`, thus `nsin(2pie n!)` will oscillate between `+-n`, and `n rarr oo` the amplitude of these oscillation will increase without bound.