a1*a2*a3*……*an= n²
a1*a2*a3*……*a(n-1)= (n-1)²
将第一式除第二式,得:an=n²/(n-1)²,an>0
同理：a(n+1)=(n+1)²/n²
那么：a(n+1)/an = [(n+1)²/n²] / [n²/(n-1)²]
= (n+1)²(n-1)²/ (n²)²
= [(n²-1)/n²]²
= (1- 1/n²)² a(n+1)