Question

已知数列{a n }的各项为正数，前n项和为S n ，若{log 2 a n }是公差为-1的等差数列，且 lim n→

Answer 1

∵{log ₂a _n}是公差为-1的等差数列

∴log ₂a _n=log ₂a ₁-n+1

∴ a n = 2 ( log 2 a 1 -n+1)

∴ s n = a 1 (1+

1

2 +…+

1

2 n-1 )=

a 1 [1- (

1

2 ) 2 ]

1-

1

2 ，

lim

n→∞ S n =

5

3

∴ a 1 =

5

6 ．

故选B．