等差数列等幂和的递推公式  

Recurrence Formula of the Sum of Equal Power Series of an Arithmetic Sequence

作　　者：施俊[1] 

机构地区：[1]江苏理工学院数理学院,江苏常州213001

出　　处：《江苏理工学院学报》2014年第2期76-80,共5页Journal of Jiangsu University of Technology

摘　　要：利用自然数等幂和的Bernoulli数公式和二项式展开定理证明了等差数列前n项等幂和Sr(a1,d,n)为n的r+1次多项式r∑j=0bjnr+1-j,同时利用线性方程组导出等差数列的一个避开Bernoulli数的等幂和递推公式。The sum of equal power series Sr（a1,d,n） of the first n terms of any arithmetic sequence can be written a r＋1 degree polynomial ∑j=0^rbjn^r＋1-j,using the Bernoulli numbers and the Binomial expansion theo-rem.Moreover,a recurrence formula of the sum of equal power series of arithmetic sequence is derived,using linear system of equations and avoiding Bernoulli numbers.

关 键 词：等差数列 等幂和 BERNOULLI数 线性方程组 递推公式 

分 类 号：O156.4[理学—数学]