lim(n>∞)pi/n(cos^2pi/n+cos^2 2pi/n+…+cos^2 n-1pi/n)=

lim(n>∞)pi/n(cos^2pi/n+cos^2 2pi/n+…+cos^2 n-1pi/n)=lim(n>∞)(pi/n)*((1+cos2pi/n)/2+(1+cos4 pi/n+…+cos2 (n-1)pi/n))=lim(n>∞)(pi/n)(1/2n + cos2pi/n +cos4pi/n +.cos2(n-1)pi/n)=lim(n>∞)(pi/2 + pi/n∑(x从1到n-1)(cos(2x/n))=lim(n>∞)(pi/2+[(n/2pi)(sin(2pi*(n-1/n) - sin(2pi/n)])=(n趋于无穷时,sin0,所以只剩前一项)lim(n>∞)（pi/2）=pi/2