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,L），其前n项的k次幂之和为nkSadkn(,,)lim(,,,=Dadknx)aid()1x®0=；åéë+-ùû．i=0.%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,where a, d, k are arbitrary real numbers, n is a positive integer, x is a real variable.
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