已知公差大于零的等差数列{a n }的前n项和S n ,且满足:a 2 ?a 4 =65,a 1 +a 5 =18. (1)若1<i<21,a 1 ,a i ,a 21 是某等比数列的连续三项,求i的值; (2)设 b n = n (2n+1) S n ,是否存在一个最小的常数m使得b 1 +b 2 +…+b n <m对于任意的正整数n均成立,若存在,求出常数m;若不存在,请说明理由.
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