(Ⅰ)∵Sn=
,n∈N*,n=1时,a1=S1=
an(an+1) 2
,
a1(a1+1) 2
∴a1=1或a1=0.又an>0,∴a1=1.
由
,得2an=2(Sn?Sn?1)=
2Sn=
+an,n∈N*
a
2Sn?1=
+an?1,n≥2
a
?
a
+an?an?1,
a
∴(an+an-1)(an-an-1-1)=0,
∵an+an-1>0,∴an-an-1=1,n≥2,
∴数列{an}是以1为首项,1为公差的等差数列,
∴an=n…(6分)
(Ⅱ)bn=(2n?1)2n,
∴Mn=1?2+3?22+5?23+…+(2n?1)?2n,…①
∴2Mn=1?22+3?23+…+(2n-3)?2n+(2n-1)?2n+1…②
由①-②得?Mn=1?2+2?22+23+…+2?2n?(2n?1)?2n+1=
?(2n?1)2n+1?24?2n+2
1?2
∴Mn=(2n?3)?2n+1+6.…(12分)