an=(n!)^2/[(2n)!]an+1/an=[(n+1)!]^2/[(2n+2)!]/(n!)^2/[(2n)!]= [(n+1)!/n!]^2*[(2n)!/(2n+2)!]=(n+1)^2/(2n+1)(2n+2)lim(n→∞)an+1/an=lim(n→∞) (n+1)^2/(2n+1)(2n+2)=1/4 = [(n+1)!/n!]^2*[(2n)!/(2n+2)!]上式怎么等于下式的?=(n+1)^2/(2n+1)(2n+2)[(n+1)!/n!=[(n+1)*n*(n-1)*(n-2)……*1]/[n*(n-1)*(n-2)……*1]=(n+1)写出来就发现后面的都消了(2n)!/(2n+2)!=[(2n)*(2n-1)*(2n-2)……*1]/[(2n+2)*(2n+1)*2n*(2n-1)……*1]=1/(2n+1)(2n+2)写出来发现分子都消去了