【简答题】设数列{a n }的前n项和为S n ,且S n =(1+λ)-λa n ,其中λ≠-1,0; (I)证明:数列{a n }是等比数列. (II)设数列{a n }的公比q=f(λ),数列{b n }满足 b 1 = 1 2 ,b n =f(b n-1 )(n∈N * ,n≥2)求数列{b n }的通项公式; (III)记λ=1,记 C n = a n ( 1 b n -1) ,求数列{C n }...
【简答题】已知f(x)=(x-1) 2 ,数列{a n }是首项为a 1 ,公差为d的等差数列;{b n }是首项为b 1 ,公比为q(q∈R且q≠1)的等比数列,且满足a 1 =f(d-1),a 3 =f(d+1),b 1 =f(q+1),b 3 =f(q-1). (Ⅰ)求数列{a n }和{b n }的通项公式; (Ⅱ)若存在c n =a n ?b n (n∈N * ),试求数列{c n }的前n项和;...