f(x)=(2x+3)/3x
=2/3+1/x
所以an=f[1/a(n-1)]
=2/3+1/[1/a(n-1)]
=2/3+a(n-1)
an-a(n-1)=2/3
所以an为d=2/3的等差数列.
所以an=a1+(n-1)d
=1+2(n-1)/3
=2n/3+1/3