Question

如何证明（2n）的阶乘/2的n次方乘以n的阶乘=1.3.5.……（2n-1)

Answer 1

2n!=1*2*3*4*...*2n

n!=1*2*3*4*...*n

2^n=2*2*2*2*2*..*2(n个2)

所以2^n*n!=1*2*3*...*n*2*2*2*..*2(n个2)

=(1*2)*(2*2)*(3*2)*...*(n*2)

=2*4*6*8*...*2n

所以2n!/(n!*2^n)=1*2*3*4*...*2n/(2*4*6*8*...*2n)

=1*3*5*7*...*(2n-1)