中算家的游戏规则最终导致清代级数论的饱和。
The rules of the game in Chinese arithmetic made Qing-times series saturated at last.
割圆连比例不可能为清代级数论提供坚实的基础。
The cyclotomic continued proportion is impossible to furnish Qing-times series with a solid basis.
有学者已就清代级数论的一组初始条件作了不少解释，至于它被近代级数论完全取代的决定因素则未论及。
The initial conditions of Qing-times series have been explored by many scholars, however, the reasons why it was entirely replaced by modern series have not been discussed yet.
借鉴数论方法中的密率论，给出判别正项级数敛散性的密率判别法，此方法特别适用于判定一些较难或不能给出通项表达式的级数的敛散性。
By using the density theory of theories of Numbers, the article gives the density discrimination method determining the convergence and divergence characteristic of the positive term series.
利用解析数论工具证明了算术级数数列中素数幂分布的若干结果，这些结果在提供RBIBD设计与PMD设计的渐近存在性定理的精确定界时具有重要作用。
We present several theorems on the distribution of prime powers. These results play a very important role in providing explicit bounds for the asymptotic existence theorems of RBIBD and PMD.
利用解析数论工具证明了算术级数数列中素数幂分布的若干结果，这些结果在提供RBIBD设计与PMD设计的渐近存在性定理的精确定界时具有重要作用。
We present several theorems on the distribution of prime powers. These results play a very important role in providing explicit bounds for the asymptotic existence theorems of RBIBD and PMD.
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