I've been trying to solve this limit analytically, but I can't figure out how to manipulate the expression in such a way so that I can plug in infinity for n without getting an indeterminate form:

lim n * sqrt(2-2cos(2pi/n))

n ->infinity

From entering this limit into the calculator, I get 2pi, which I know is the correct answer. So how might I solve this limit analytically?

Also, bear in mind that this is in the precalc section, so I'm familiar only with with limit properties and such.

Thanks a lot!