用函数极限求等差数列前n项的方幂和

Using function limit process to find power sum of the precedingn terms of a arithmetic progression

提出了一个求等差数列方幂和的极限法.构造了一个函数D(a,d,k,n;x),其中:a,d,k为任意实数;n为正整数;x为实变量.证明了对任意等差数列a+(i-1)d(i=1,2,3,…),其前n项的k次幂之和为Sn(a,d,k)=limx→0(a,d,k,n;x)=nΣi=0[a+(i-1)d]k.

Put forward a new method to find power sum of a arithmetic progression by using of limit process. A function D（a, d, k, n, x） was constructed, wherea, d, k are arbitrary real numbers, n is a positive integer, x is a real variable. Also proofed that to arbitrary arithmetic progression a ＋ （i - 1）d （ i = 1, 2, 3, ... ）, the k - power sum of its preceding n terms is Sn（a,d,k）=limx→0（a,d,k,n;x）=nΣi=0[a＋（i-1）d]k