| 自然数等幂和的一种解法与推广 |
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| 引用本文： | 杨杰. 自然数等幂和的一种解法与推广[J]. 安庆师范学院学报(自然科学版), 2014, 0(1): 29-31 |
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| 作者姓名： | 杨杰 |
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| 作者单位： | 南京理工大学电子工程与光电技术学院; |
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| 摘 要： | 本文运用等比数列求和公式及求导法则，得到了∑n k＝1 km ，∑n k＝1[a ＋（k -1）d]m，∑n k＝1[a ＋（k -1）d]mxa＋（k-1）d-1（m，n∈瓔，a，d∈瓗）等若干等幂和公式，为一类等幂和级数提供了一种简洁计算方法。
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| 关 键 词： | 等幂和 等比级数 等差级数 |
A Solution to the Equal Powers Sum of Natural Number and Its Generalization |
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| YANG Jie. A Solution to the Equal Powers Sum of Natural Number and Its Generalization[J]. Journal of Anqing Teachers College(Natural Science Edition), 2014, 0(1): 29-31 |
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| Authors: | YANG Jie |
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| Affiliation: | YANG Jie ( School of Electronic and Optical Engineering, Nanjing University of Science and Technology, Nanjing 210094, China) |
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| Abstract: | On the basis of the summation formula of ratio of equality series and derived rules of functions, this paper deduces a few formulae of equal powers sum ,such as∑n k=1 km,∑n k=1 [a ＋（k -1）d]m,∑n k=1 [a ＋（k-1）d]mxa＋（k-1）d-1 where m,n∈,a, d∈,etc.It provides a concise method for the sum of equal powers. |
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| Keywords: | equal powers sum ratio of equality series arithmetic sequence |
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