【简答题】已知等比数列{a n }的公比大于1,S n 是数列{a n }的前n项和,S 3 =39,且a 1 , 2 3 a 2 , 1 3 a 3 依次成等差数列. (Ⅰ)求数列{a n }的通项公式; (II)若数列{bn}满足:b 1 =3,b n =a n ( 1 a 1 + 1 a 2 +…+ 1 a n-1 )(n≥2),求数列{b n }的前n项和T n .
【简答题】已知等差数列 { a n n } 满足a 1 =1,a 3 =6,若对任意的n∈N * ,数列{b n }满足b n ,2a n+1 ,b n+1 依次成等比数列,且b 1 =4. (1)求a n ,b n (2)设S n =(-1)b 1 +(-1) 2 b 2 +…+(-1) n b n ,n∈N*,证明:对任意的n∈N*, | S n |> 1 2 b n .