等幂迭乘和的扩展及求和公式证明

The expansion of sum of equal powers and the demonstration of summation formula

利用公式∑k=0Cnkf(k)rk扩展了等幂迭乘和的表示范围.以矩阵为工具,研究此类数列的求和公式,得出f(k)=km,r=1,-1,exp(iθ)时的结论.

The range of sum of equal powers was extended by ∑nk=0f（k）rkCkn and the summation formula of such series was derived out simply and directly by using matrix.At last,conclusions on f（k）=km and r=1,-1,exp（iθ） are given.