Is sum of sin(pi/n) DV or CV?

Question

I don't understand why it is DV.

Answer 1

sin pi/1 = 0
sin pi/2 = 1
sin pi/3 = .866
sin pi/4 = .707 and pi/4 = .785
sin pi/5 = .587 and pi/5 = .628
.
.
.
sin pi/100 = .0314107 and pi/100 = .0314159
as we know sin x ---> x as x gets big
so terms get progressively smaller like 1/n (which converges to e) so I think it converges.

Answer 2

1/n! converges to e
1/n does not converge!!!!
every term in our series sin (pi/n) is bigger than 1/n
So it does NOT converge!!
(This is what I get for counting on my aged memory)