∵ [AnA(n+1)]^=[A(n+1)A(n+2)][A(n-1)An], ∴ A(n+2)/A(n+1)=An/A(n-1)=…=A2/A1=r, An=A1·r^(n-1)=r^(n-1), A(2n-1)=r^(2n-2),A(2n)=r^(2n-1), ∴ Bn=r^(2n-2)-r^(2n-1)=(1-r)(r^)^(n-1)
Sn=(1-r)[1-r^(2n)]/(1-r^)=[1-r^(2n)]/(1+r)
Sn>Bn, [1-r^(2n)]/(1+r)>(1-r)(r^)^(n-1), r^(2n)<(r^)/(1-2r^),
若0<r<1, 0<r^(2n)<1≤(r^)/(1-2r^), ∴ 1/3≤r^<1/2, √3/3≤r<√2/2,
若r>1, 1≤r^(2n)<(r^)/(1-2r^),无解.
∴ r的取值范围是[√3/3,√2/2)