证明：由bn+1 • log9

an+1+1

an+1-1

=1⇒bn+1 • log9

1 2 (an+ 1 an )+1

1 2 (an+ 1 an )-1

=1⇒bn+1 • log9(

an+1

an-1

)2=1⇒2bn+1 • log9

an+1

an-1

=1又bn • log9

an+1

an-1

=1

∴bn+1=

1

2

bn

又n=1时，b1 • log9

a1+1

a1-1

=1⇒b1=2

∴{b_n}为等比数列，b₁=2，q=

1

2

，∴bn=2 • (

1

2

)n-1=(

1

2

)n-2