1.
Sn=3/2(an-1)
S(n+1)=3/2[a(n+1)-1]
S(n+1)-Sn
=3/2[a(n+1)-1]-3/2(an-1)
=3/2a(n+1)-3/2an
=a(n+1)
1/2a(n+1)=3/2an
a(n+1)=3an
{an}是公比为3的等比数列
首项a1=S1=3/2(a1-1)
2a1=3a1-3
a1=3
∴an=3×3^(n-1)=3^n
2.
an-a(n-1)=2^(n-1)
a(n-1)-a(n-2)=2^(n-2)
……
a3-a2=2^2
a2-a1=2^1
把它们都加起来:
an-a1=2^1+2^2+……+2^(n-2)+2^(n-1)
an=a1+2^1+2^2+……+2^(n-2)+2^(n-1)
=2+2^1+2^2+……+2^(n-2)+2^(n-1)
=2^n
3.
令an