已知数列{a n }满足a 1 =1, a n-1 a n = a n-1 +1 1- a n (n∈N * ,n>1). (1)求证:数列 { 1 a n } 是等差数列; (2)求数列{a n a n+1 }的前n项和S n ; (3)设f n (x)=S n x 2n+1 ,b n =f' n (2),求数列{b n }的前n项和T n .
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