在新课程人教A版数学中,有这样的例题与习题:例题若数列{1/(3n-2)(3n+1)}的前n项和是Sn,计算S1、S2、S3,根据计算结果推测计算Sn的表达式并给出证明.习题若数列{1/n(n+1)}的前n项和是Sn,计算S1、S2、S3,推测计算Sn的公式并给出证明.由此引发出这样 In the new curriculum, people teach A version of mathematics, there are such examples and exercises: Example If the first n series of sequence {1 / (3n-2) (3n + 1)} and is Sn, calculate S1, S2, S3, according to The calculation result presupposes the calculation of Sn and gives a proof. Exercises If the first n terms of the series {1 / n (n + 1)} and is Sn, calculate S1, S2, S3, speculate the formula for calculating Sn and give a proof This leads to this