6α-2αβ+6β=3
6(α+β)-2αβ=3
6a(n+1)/an -2/an=3
a(n+1)=(1/2)an+(1/3)
a(n+1)-(2/3)=(1/2)an+(1/3)-(2/3)=(1/2)[an-(2/3)]
所以：{an-2/3}是公比为1/2的等比数列
a1=7/6
∴a1-2/3=1/2
an-2/3=1/2*(1/2)^(n-1)
an=(1/2)^n+2/3
Sn=a1+a2+...+an
=(1/2-1/2^(n+1))/(1-1/2)+2n/3
=1-1/2^n+2n/3
如果本题有什么不明白可以追问,