设数列{An}的首项是A1=A≠1/4,且A（n+1）=1/2*An（当n为偶数时）或An+1/4（当n为奇数时）记Bn=A（2n-1）-1/4,n=1、2、3……（1）求A2、A3（2）判断{Bn}是否为等比数列,并证明你的结论

1）求A2、A3
A2=A1+1/4=A+1/4
A3=1/2A2=1/2A+1/8
2）B（n+1）/Bn
=[A（2n+1）-1/4]/[A（2n-1）-1/4]
=（1/2*A2n-1/4）/[1/2*A(2n-2)-1/4]
=（A2n-1/2）/[A(2n-2)-1/2]
=[A(2n-1)+1/4-1/2]/[A(2n-3)+1/4-1/2]
=[A(2n-1)-1/4]/[A(2n-3)-1/4]
=Bn/B(n-1)
因为B（n+1）/Bn=Bn/B(n-1)，且B1=A3-1/4=1/2A-1/8≠0
所以Bn为等比数列
或者1.
A2=A1+1/4=1/2
A3=A2*1/2=1/4
2.
Bn=A（2n-1）-1/4 A(2n-1)=A[(2n-2)+1] (2n-2)为偶数，所以
=A(2n-2)*1/2-1/4 A(2n-2)=A[(2n-3)+1] (2n-3)为奇数，所以
=[A(2n-3)+1/4]*1/2-1/4
=1/2A(2n-3)-1/8
=1/2[A(2n-3)-1/4]
=1/2Bn-1
所以是等比数列

1.
A2=A1+1/4=1/2
A3=A2*1/2=1/4
2.
Bn=A（2n-1）-1/4 A(2n-1)=A[(2n-2)+1] (2n-2)为偶数，所以
=A(2n-2)*1/2-1/4 A(2n-2)=A[(2n-3)+1] (2n-3)为奇数，所以
=[A(2n-3)+1/4]*1/2-1/4
=1/2A(2n-3)-1/8
=1/2[A(2n-3)-1/4]
=1/2Bn-1
所以是等比数列

1）求A2、A3
A2=A1+1/4=A+1/4
A3=1/2A2=1/2A+1/8
2）B（n+1）/Bn
=[A（2n+1）-1/4]/[A（2n-1）-1/4]
=（1/2*A2n-1/4）/[1/2*A(2n-2)-1/4]
=（A2n-1/2）/[A(2n-2)-1/2]
=[A(2n-1)+1/4-1/2]/[A(2n-3)+1/4-1/2]
=[A(2n-1)-1/4]/[A(2n-3)-1/4]
=Bn/B(n-1)
因为B（n+1）/Bn=Bn/B(n-1),且B1=A3-1/4=1/2A-1/8≠0
所以Bn为等比数列