无穷级数

Definition The infinite series converges and has sum if the sequence of partial sums converges to ,that is .If diverges, then the series diverges. A divergent series has no sum.

定义如果级数的部分和数列有极限，即，则称无穷级数收敛，这时极限叫做这级数的和，并写成；如果没有极限，则称无穷级数发散。

Energy density and particle density in high energy heavy-ion collisions are calculated with infinite series expansion method and Gauss-Laguerre formulas in numerical integration separately, and the results of these two methods are compared, the higher terms and linear terms in series expansion are also compared.

分别用无穷级数展开方法和数值积分计算中的高斯拉盖尔求积法对高能重离子碰撞中能量密度和粒子密度数值进行计算，并对结果及级数展开中的高次项和一次项的大小进行了比较。

An infinite series that results in a finite sum is said to converge. One that does not, diverges.

一个无穷级数可求得和便称为收敛级数，若否，则称为发散级数。

An in finite series that results in a finite sum is said to converge. One that does not, diverges.

一个无穷级数可求得和便称为收敛级数，若否，则称为发散级数。

An infinite series that results in a finite sum is said to converge. One that does not, diverge s.

一个无穷级数可求得和便称为收敛级数，若否，则称为发散级数。

Pi, expressed as an infinite series and an infinite product.

丕表示，作为一个无穷级数和无穷乘积。

As analysis becoming more and more rigorous, the theory of infinite series has come into being, which promote the development of mathematics largely.With the development of infinite series as the center, with the variation of thought after t...

本文以无穷级数的发展为中心，以无穷进入数学前后思想变化为线索，系统分析了级数理论形成的历史背景，通过对主要人物工作的总结，概括了级数理论的建立及其发展的过程。

Summation of infinite series is part of the process of learning more difficult to grasp the progression part, this article summarizes the common summation of several infinite series method, as has the use of progression and the definition of sum, the use of itemized points or one differential sum, the use of split-phase elimination method of summation methods, and problem-solving steps in detail.

无穷级数的求和部分是学生学习级数过程中较难掌握的部分，本文归纳了常见的几种无穷级数的求和方法，像有利用级数和的定义求和、利用逐项积分或逐项微分法求和、利用裂项相消法求和等方法，并提出了详细的解题步骤。

According to the theory of elasticity, the displacement and stress solutions of the model is expressed in the form of the sum of two infinite series of Fourier and Fourier-Bessel functions.

通过弹性理论分析，将其位移和应力表达成富氏级数和富氏—贝塞尔级数两个无穷级数之和的形式，从而求得了对应这个模型的纤维与基体之间更为精确的理论分析解。

Where the nth term is said to be the general term of the series, moreover, the nth partical sum of the series is given by .

叫做无穷级数，简称级数，记为，即其中第项叫做劫数的一般项。称为级数(1)的部分和。

The split between the two groups can hardly be papered over.

这两个团体间的分歧难以掩饰。

This approach not only encourages a greater number of responses, but minimizes the likelihood of stale groupthink.

这种做法不仅鼓励了更多的反应，而且减少跟风的可能性。