无理数可以被定义为无限不循环小数，在许多工作中，我们只使用其近似值。对研究一个无理数的近似值而言，这个无理数及其倒数的级数展开式均具有重要意义。超几何方法、差分算子理论和WZ方法是组合数学中常用的方法。本项目旨在利用这三种方法，系统地探索圆周率、Euler-Mascheroni 常数、素数的1/n（n是大于1的自然数）次方及它们的倒数的级数展开式, 并且考虑其中快速收敛的级数展开式在圆周率、Euler-Mascheroni常数与素数的1/n次方的近似值研究中的应用。

In many work, we use only the approximate values of irrational numbers which can be defined as the infinite non-repeating decimals. Series expansions of the irrational number and its reciprocal are significant to the research for the approximate value of an irrational number. The hypergeometric method, difference operator theory and WZ method are the regular methods in combinatorics. The purpose of the project is to explore systematically the series expansions of ratio of the circumference, Euler-Mascheroni constant, primes to the opwer of 1/n where n is a natural number greater than 1 and their reciprocals in terms of the three methods just mentioned, and consider the applications of the rapid convergence series expansions of them to the study for the approximate values of ratio of the circumference, Euler-Mascheroni constant and primes to the opwer of 1/n.