Re: Why is this limit 0?

["Chip Eastham"]

TCL wrote:
> Let  p(n)= int_0^pi  | sin(n+ 0.5)x| /  sin (0.5 x)  dx.
> I am trying to prove that
> lim    p(n)/ ln n   = 0.
>
> I am able to prove  lim sup p(n)/ ln n  is finite, but of course that is not
> good enough.

I suspect you need only analyze the behavior of the
integrand in the neighborhood of x = 0, since away
from zero the integrand is bounded independent of n
and hence that portion of p(n), when divided by ln(n),
tends to zero.

regards, chip