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1·Convergence and divergence of infinite series depend upon this concept.

无穷级数的收敛性与发散性与此概念有关。

2·An exact solution is developed in terms of doubly infinite series, using a stress-function approach.

利用应力函数法将精确解按双无穷级数展开。

3·Property 3 Deleting, adding and altering the finite terms of the infinite series keep the convergence of the series.

性质3在级数中去掉、加上或改变有限项，不会改变级数的收敛性。

4·This course mainly includes: vector algebra and analytic geometry in space, multivariable calculus and infinite series.

本课程主要内容包括：向量代数与空间解析几何、多元函数微积分、无穷级数等。

5·He believed in an infinite series of times, in a dizzily growing, ever spreading network of diverging, converging and parallel times.

他认为时间有无数系列，背离的、汇合的和平行的时间织成一张不断增长、错综复杂的网。

6·More than 100 terms required in an infinite series are examined to compute all physical quantities under a tolerance of less than 0.005.

本文以误差精度在0.005 以下要求 下，测试此无穷级數之最合适之有限项數，发现需要100 项能达到要 求。

7·However, if the principle is assumed, it is surely incongruous to postulate a first cause as a way of escaping from the coils of an infinite series.

然而，如果承认这一原则，那么，假设某种第一推动力以避开无限系列造成的麻烦肯定是不合理的。

8·In this paper, new criterion of convergence and divergence for infinite series is given by means of the convergence and divergence of infinite integral.

利用无穷积分的敛散性给出了无穷级数敛散性的一个新的判别法。

9·This paper gives a theoretical and analytical solution of the dynamic response for long gas pipeline in the form of infinite series with Bessel functions.

本文以贝塞尔函数级数和的形式，给出了动态特性的理论解析解。

10·Cyclotomic continued proportion was the principal method for studies on infinite series in the Qing Dynasty, which we still have to go into a step further.

割圆连比例曾是清代无穷级数研究中所用的主要方法，但对它的研究目前还不够充分。