已知：数列{an},满足a1＝2，[a(n+1)]/an=n/(n+1),则通项an＝

a(n+1)={[a(n+1)]/[a(n)]}*{[a(n)]/[a(n-1)]}....*{[a(2)]/[a(1)]}*[a(1)]
=n/(n+1)*(n-1)/n....*1/2*2
=2/(n+1)
所以an=2/n

很简单啦
a2=1/2 *a1=1/2 *a1=2/2
a3=2/3 *a2=2/3 *(1/2 *a1)=2/3
..同理
an=...=a1/n=2/n

an＝(n-1)/n*a(n-1)
=(n-1)/n*(n-2)/(n-1)*a(n-2)
=……(n-1)/n*(n-2)/(n-1)*……*1/2*a1
=1/n*a1
=2/n