文[1]给出了等差(比)数列前n项和的一个性质:设等差数列{an}公差为d,前n项和为Sn,则Sm+n=Sm+Sn+mnd.设等比数列{an}公比为q,前n项和为Sn,则Sm+n=Sm+Snqm.在其基础上,经笔者探究得出如下几个推广性质:定理1设等差数列{an}公差为d,前n项和为Sn,则Sm+n+l=Sm+Sn+Sl+(mn+ml+nl)d.证? [1] gives a property of the sum of the first n terms of the arithmetic difference (ratio) series: Let the tolerance series {an} have a tolerance of d, and the first n terms are Sn, then Sm+n=Sm+Sn+mnd. Suppose that the ratio {a} is a common ratio of q, and the first n terms are Sn, then Sm+n=Sm+Snqm. Based on it, the following generalized properties are obtained by the author’s investigation: Theorem 1 Sets the arithmetic series The {an} tolerance is d, and the first n terms are Sn, then Sm+n+l=Sm+Sn+Sl+(mn+ml+nl)d.