(Ⅰ)令x1=x2=0,
由③知f(0)=2f(0)-2?f(0)=2;
(Ⅱ)任取x1x2∈[0,1],且x1<x2,
则0<x2-x1≤1,∴f(x2-x1)≥2
∴f(x2)-f(x1)=f[(x2-x1)+x1]-f(x1)
=f(x2-x1)+f(x1)-2-f(x1)=f(x2-x1)-2≥0
∴f(x2)≥f(x1),则f(x)≤f(1)=3.
∴f(x)的最大值为3;
(Ⅲ)由Sn=?
(an?3)知,1 2
当n=1时,a1=1;当n≥2时,an=?
an+1 2
an?11 2
∴an=
an?1(n≥2),又a1=1,∴an=1 3
1 3n?1
∴f(an)=f(
)=f(1 3n?1
+1 3n
+1 3n
)=f(1 3n
)+f(2 3n
1 3