In this paper,we firstly modified the mistake in reference of Bennett,then using Strmer s theorem of the solutions of Pell equation,and a deep result of privitive divisor of Bilu,Hanrot and Voutier,we proved that there is no exist four distinct triangular numbers in geometric progression,therefore we sovled the question of Sierpinski on triangular numbers.
基于三角数问题的研究目前非常活跃,最近,Bennett宣布解决了由Sierpinski提出的一个三角数猜想问题,本文指出了Bennett文中的错误,并利用Pell方程解的性质的St rmer定理以及Bilu,Hanrot和Voutier的关于本原素因子的深刻结论,证明了在一列几何级数中,不存在4个相异的三角数,完整地解决了Sierpinski的问题。
when n=2~(r+1)-1,it can be expressed by geometric progression ∑ni=0x~i=∏rj=0(1+x~(2~j)).
当n=2r+1 -1时,几何级数可以表示为:∑ni=0xi=∏rj=0(1+x2j)。
By using summation algorithms of hypergeometric series,the author got a series of summations of hypergeometric series which widen the research results of ZHANG Xiang-de,TAO Ching-qi.
通过运用超几何级数的求和算法 ,得到一系列超几何级数的求和公式 ,从而拓展了ZHANGXiang de ,TAOChing qi的一系研究结果 。
Several results of q- analogue of basic hypergeometric series;
基本超几何级数q-模拟的几个结果
The evaluations of a class of basic hypergeometric series;
一类基本超几何级数的估计
By using a simple algorithm for the summation of basic hypergeometric series, summation formulas for some basic hypergeometric series are obtained.
本文运用基本超几何级数求和的一个简单算法，求得一些基本超几何级数的求和公式。
Several results of q- analogue of basic hypergeometric series;
基本超几何级数q-模拟的几个结果
Achieve exponential growth in the quantity of goods
在商品数量上实现了几何级数/指数级的增长
1-4-16-64-256- is the start of a geometric progression.
1-4-16-64-256-是一个几何级数的开始。
Population can increase in a geometric ratio.
人口可以按几何级数增长。
Population is increasing in that country in a geometrical progression.
那个国家的人口正以几何级数增长。
The Abel Lemma on Summation by Parts and Classical Hypergeometric Series;
Abel分部求和法与经典超几何级数
Elliptic Well-Poised Bailey Chains and Transformations of Hypergeometric Series;
椭圆Well-Poised Bailey链与超几何级数变换
Hypergeometric Series Method for Riemann-Zeta Function and Combinatorial Identities;
Riemann-Zeta函数的超几何级数方法和组合恒等式
The Operator Method, Cauchy Method and Inversion Techniques for Basic Hypergeometric Series;
基本超几何级数的算子方法、Cauchy方法与反演技巧
The Proof of the WZ Method for Some Hypergeometric-type Series Identities
若干_2F_1型超几何级数恒等式的WZ方法证明
On basis of the results of reference, in this paper, the author got the summation formula of several basic bypergeometric series.
在文献［］［］［］得结论基础上，又得到了几个基本超几何级数的求和公式。
The paper describes three determination methods of alpha activity ratio used at our laboratory, namely geometric progression method, extrapolation method and curve fitting method.
采用了3种α放射性比的测定方法:几何级数法、推法和曲线拟合法。
Third, the creation, consumption and communication of content have increased exponentially.
第三，内容上的创新、费、播正在以几何级数的速度增长。
an arithmetic(al) [a geometric(al)] progression
算术 [几何] 级数,等差 [等比] 级数
Geometrical Explication of Fourier Series about a Function;
函数展开成Fourier级数的几何解释
GEOMETRICAL FIT OF EXPERIMENTAL VARIOGRAMWITH DOUBLE STRUCTURES
二级套合结构实验变差函数的几何拟合
The key to divine harmonic proportion( sacred geometry) is the relationship between progression of growth and proportion.
神的调和比例（的几何学）键是生长级数和比例间的联系。
The Research for Geometry、Potential Function、Energy Level Distribution and Electronic Properties of Au、Cu、Y Micro-clusters;
金、铜、钇小团簇的几何结构、势能函数、能级分布和电子特性研究