例说n项和数列极限的几种求法 |
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引用本文: | 何美,刘小川. 例说n项和数列极限的几种求法[J]. 高等数学研究, 2016, 0(3): 37-39. DOI: 10.3969/j.issn.1008-1399.2016.03.014 |
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作者姓名: | 何美 刘小川 |
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作者单位: | 山西大同大学 数学与计算机科学学院,山西 大同,037009 |
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基金项目: | 山西大同大学教改课题项目(XJG2015201) |
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摘 要: | 有限个数列和的极限一般可用"数列和的极限等于数列极限的和"的运算法则来计算,而对于n项和数列的极限不能采用和的运算法则.针对此问题,文中利用迫敛性、定积分、幂级数和函数性质以及Fourier级数和函数得到了求此类极限的方法.
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关 键 词: | n项和数列 迫敛性 定积分 幂级数 Fourier级数 |
Several Explorations in Resolving Limit of Number Sequence of the Sum of n Terms by Examples |
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Abstract: | To calculate the limit of the sum of limited sequence always uses the rule ‘the limit of the sum equals the sum of the limit’ , but this rule cannot resolve the limit of the number sequence of the sum of n terms. Given several methods using squeeze theorem, definite integral, properties of sum function of power series and the sum function of Fourier series to resolve such limit. |
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Keywords: | sequence of the sum of n terms squeeze theorem definite integral power series Fourier series |
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