1. The problem statement, all variables and given/known data Evaluate the limit 1 1 1 lim ∫ ∫ ... ∫ cos^2((pi/2n)(x1 + x2 +... xn))dx1 dx2 ... dxn 0 0 0 n→∞ 2. Relevant equations Well, I know that we can change this using a double angle rule, so that the integrals become 1/2 + 1/2 cos (2*pi/2n)(x1 + x2 +... xn))dx1 dx2 ... dxn and the integral over the 1/2 just becomes 1/2, but the other side baffles me. 3. The attempt at a solution My professor tried to do this, but I don't agree with his methodology. When he integrated it, he got pi/n out front, and if you keep integrating, this would go to pi^n / n^n . However, the integral should produce n^n / pi^n if I'm not mistaken, meaning this would diverge to infinity, and not go to zero like he said. Any ideas?