由于探索性问题能够有效地考查学生的数学素质 ,因而成为高考命题的热点 .下面仅就数列中探索性问题的求解策略作些归纳 ,以期抛砖引玉 .一、利用公式直接求解例 1　是否存在常数a ,b ,c使等式 1·n+ 2 · (n -1) +… + (n -1) ·2 +n·1=an3+bn2 +cn对任意的n∈N 恒成立 ?证明 Because the exploratory problem can effectively examine students’ mathematics quality, it has become a hot spot for college entrance examination propositions. The following is only a summary of the solution strategies of the exploratory problems in the series, with a view to throwing bricks and jade. First, using the formula to directly solve the case 1 whether there is a constant a ,b ,c such that the equation 1·n+ 2 ·(n -1) +... + (n -1) ·2 +n·1=an3+bn2 +cn holds for any n∈N constant?