Question

求证(n+1)(n+2)(n+3)……(n+n)=2^n*1*3*……*(2n-1)

Answer 1

n=1成立,

n=k 成立,

则n=k+1时

左边=(n+2)(n+3)……(n+n)（n+n+1)(n+1+n+1)=

=2^n*1*3*……*(2n-1)（n+n+1)(n+1+n+1)/(n+1)=

=2^n*1*3*……*(2n-1)（2n+1)*2=

=2^(n+1)*1*3*……*(2n-1)（2n+1)=右边

证毕