| 等差数列前n项等幂和计算公式及算法实现 |
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| 引用本文： | 金晶,杨婷娜,朱伟义.等差数列前n项等幂和计算公式及算法实现[J].渭南师范学院学报,2012(2):25-30. |
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| 作者姓名： | 金晶 杨婷娜 朱伟义 |
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| 作者单位： | 浙江师范大学数理信息学院,浙江金华,321004 |
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| 基金项目： | 基金项目:国家自然科学基金资助项目 |
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| 摘 要： | 首先利用微分算子以及Bernoulli数巧妙地得到了求任意等差数列前n项等幂和的一个简洁且更一般的计算公式，同时利用导出公式分别给出了前11个自然数等幂和公式和前n个奇数的等幂和公式，然后利用Maple7给出计算程序．
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| 关 键 词： | Bernoulli数 等差数列 等幂和 计算程序 |
Calculation Formula of the Sum of Powers of the First n Terms of an Arithmetic Sequence and Its Algorithm |
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| JIN Jing,YANG Ting-na,ZHU Wei-yi.Calculation Formula of the Sum of Powers of the First n Terms of an Arithmetic Sequence and Its Algorithm[J].Journal of Weinan Teachers College,2012(2):25-30. |
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| Authors: | JIN Jing YANG Ting-na ZHU Wei-yi |
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| Institution: | (College of Mathematics,Physics and Information Engineering,Zhejiang Normal University,Jinhua 321004,China) |
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| Abstract: | At first,the paper gives a general formula of the sum of powers of the first n terms of any arithmetic sequence using the differential operator and the Bernoulli numbers,specifically gives the Sum of powers of the first n natural numbers and first n odd numbers,and then presents a calculating program of the general formula. |
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| Keywords: | Bernoulli numbers arithmetic sequence sum of powers calculating program |
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