# Sequence question.

1. Feb 20, 2012

### cragar

1. The problem statement, all variables and given/known data
Does $nsin(2\pi en!)$
converge and if so what does it converge to.
this is a sequence and n is a positive integer.
3. The attempt at a solution
My teacher gave us a hint and to write e in a Taylor series.
$nsin(2\pi (1+1+\frac{1}{2!}+\frac{1}{3!}.....)n!)$
so we could multiply the n! through to the e stuff. And then look for a pattern their to see what it converges to.

2. Feb 20, 2012

### Dick

Well, what are your thoughts? I see a bunch of stuff that is a multiple of 2pi in the sin function. But I also see a bunch of stuff that's not.

Last edited: Feb 21, 2012
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