4/3×6/5×8/7×······×(2n+2)/(2n+1)求积
问题描述：
4/3×6/5×8/7×······×(2n+2)/(2n+1)求积
答
原式
=(4*6*...*(2n+2))/(3*5*...*(2n+1))
=(4*6*...*(2n+2))^2/(3*4*5*...*(2n+2))
=2^2n*(2*3*...*(n+1))^2/(3*4*5*...*(2n+2))
=2^2n*((n+1)!)^2/((2n+2)!/2)
=2^(2n+1)*((n+1)!)^2/(2n+2)!
答
2^(2n+1)[(n+1)!]^2/(2n+2)!