摘要
本文采用组合数学的方法，利用第二类Ｓｔｉｒｌｉｎｇ数和Ｂｅｒｎｏｕｌｌｉ数给出级数 sum for k=1 to ∞ k^mξ（ｋ），sum for k=1 to ∞ k^mξ（２ｋ）及sum for k=1 to ∞（２ｋ＋１）ｍξ（２ｋ＋１）（其中ｍ≥１，ξ（ｘ）＝ξ（ｘ）－１） 的求和公式．这些公式表述简洁并有鲜明的规律性。
In this paper, by means of combinatorial mathematics and using Stirling number of second kind and Bernoulli number summation formulas of series (2k)and arc given. These formulas are sum for k=1 to ∞ k^mξ（ｋ），sum for k=1 to ∞ k^mξ(2k)and sum for k=1 to ∞(2k+1)ｍξ(2k+1)（where m≥1，ξ(x)=ξ(x)-1) succinct expressed and they have clear-cut regularity.
