1问题提出最近听了一节“数列求和”的校内公开课,上课老师讲到:“对于数列{1/(an～2+bn+c)}(a≠0),只要an2+bn+c能分解为两个多项式的乘积,则数列{1/(an～2+bn+c)}的前n项和就可采用裂项法求和.”果真如此吗?我们知道裂项的最终目的是 1 Problem We recently heard an open class in the school of “summation of numbers”, class teacher said: “For the series {1 / (an ~ 2 + bn + c)} (a ≠ 0), as long as an2 + bn + c can be decomposed into the product of two polynomials, then the first n terms of the sequence {1 / (an ~ 2 + bn + c)} can be summed using the fission method. ”Is this true? The ultimate goal of the split is