0 < ((2n-1)!/(2n)!) ^2
=[1*3*3*5*5*...*(2n-3)*(2n-1)*(2n-1)] *【(2n+1)/(2n+1)】/[2*2*4*4*...*2n*2n]
=[1*3/2*2]*[3*5/4*4]*[5*7/6*6]*...*[(n-1)(n+1)/n^2] /(2n+1)
∵ [(k-1)(k+1)/k^2 < 1∴
< 1/(2n+1)-->0(n->∞时)
∴ lim(n->∞) ((2n-1)!/(2n)!) = 0