2Sn+1=an(2an+1)
Sn=an^2+an/2-1/2
S1=a1=a1^2+a1/2-1/2
a1^2-a1/2-1/2=0
a1=1,a1=-1/2(不符合题意,舍去)
an=Sn-S(n-1)=an^2+an/2-a(n-1)^2-a(n-1)/2
an^2-a(n-1)^2-an/2-a(n-1)/2=0
[an-a(n-1)-1][an+a(n-1)]=0
∵数列an中各项均为正数
∴an-a(n-1)-1=0
an-a(n-1)=1
∴an是首项为1,公差为1的等差数列
an=1+n(n-1)/2
Sn=n(n+1)/2