Question

等比数列an中a2=27a3=243若bn=log3 an求1/bn bn+1的前n项和sn

Answer 1

a2=27

a3=243

公比q=9 a1=3 ∴an=3*9^(n-1)=3^(2n-1) bn=2n-1 b(n+1)=2n+1

1/bn bn+1=1/(2n-1)(2n+1) 裂项 =1/2*(1/(2n-1)-1/(2n+1))

Sn=1/2*(1-1/(2n+1))=n/(2n+1)