a(n+1)=f(an)=an/(an+3)
an*a(n+1)+3a(n+1)=an
1/a(n+1)=3/an+1
1/a(n+1)+1/2=3(1/an+1/2)
所以{1/an+1/2}是公比为3的等比数列
1/an+1/2=(1/a1+1/2)*3^(n-1)=(3/2)*3^(n-1)=(1/2)*3^n
1/an=(1/2)*(3^n-1)
an=2/(3^n-1)
即为所求
a(n+1)=f(an)=an/(an+3)
an*a(n+1)+3a(n+1)=an
1/a(n+1)=3/an+1
1/a(n+1)+1/2=3(1/an+1/2)
所以{1/an+1/2}是公比为3的等比数列
1/an+1/2=(1/a1+1/2)*3^(n-1)=(3/2)*3^(n-1)=(1/2)*3^n
1/an=(1/2)*(3^n-1)
an=2/(3^n-1)
即为所求