Sn=(1/4)an^2+(1/2)an-3/4
Sn-1=(1/4)an-1^2+(1/2)an-1-3/4
相减
an=(1/4)an^2+(1/2)an-(1/4)an-1^2-(1/2)an-1
化简an-an-1=2
a1=3
an=2n+1
(2)若an=2^n*bn,求数列{bn}的前n项和
bn=an/2^n
2bn-1=an-1/2^n
1/2sn-sn=an/2^n+1 -2(1/2+1/4+...+1/2^n)-3/2
Sn=(1/4)an^2+(1/2)an-3/4
Sn-1=(1/4)an-1^2+(1/2)an-1-3/4
相减
an=(1/4)an^2+(1/2)an-(1/4)an-1^2-(1/2)an-1
化简an-an-1=2
a1=3
an=2n+1
(2)若an=2^n*bn,求数列{bn}的前n项和
bn=an/2^n
2bn-1=an-1/2^n
1/2sn-sn=an/2^n+1 -2(1/2+1/4+...+1/2^n)-3/2