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已知常数 数列 的前 为 ， 且 （1）求证：数列 为等差数列； （2）若 且数列 是单调递增数列，求实数 的取值范围； （3）若 数列 满足： 对于任意给定的正整数 ，是否存在 使 若存在，求 的值（只要写出一组即可）；若不存在，说明理由.
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