n趋向正无穷时,[(2n-1)!/(2n!)]的极限是多少?

Question

n趋向正无穷时,[(2n-1)!/(2n!)]的极限是多少?

Answer 1

设 u(n)=[(2n-1)!/(2n!)] =1/2 * 3/4 * 5/6 * .* (2n-1)/(2n)
x(n)= 2/3 * 4/5 * 6/7 *.* (2n)/(2n+1)
u(n)*u(n) < u(n)*x(n) = 1/(2n+1)
0∞] =0