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已知数列 a n 满足 a 1 = 1 2 =且 a n + 1 = a n - a n 2 ( n ∈ N * ) (1)证明: 1 ≤ a n a n + 1 ≤ 2 ( n ∈ N * ) ; (2)设数列 a n 2 的前 n 项和为 S n ,证明 1 2 ( n + 2 ) ≤ S n n ≤ 1 2 ( n + 1 ) ( n ∈ N * )
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