文章着重介绍了在正项级数比较审敛法的极限形式中，用等价无穷小的方法来判别正项级数的敛散性。
This paper is mainly about recognizing convergence with the methods of infinitesimal equivalence in the limit form of convergence criterion in series of positive terms .
用比较直接的方法证明幂级数的和函数在收敛域内可以逐项微分的公式；并得到了计算傅立叶系数的一种简便方法。
A relatively direct method is expounded in this paper to prove the termwise differentiation of power series, and a simple method is expressed to calculate the Fourier coefficient.
首次用无穷级数法求解了其临界屈曲时的挠曲线微分方程，并同时用能量法给出了其临界屈曲载荷计算公式。认为能量法求解这种情况下的屈曲载荷比较困难和复杂。
The deflection differential equation of string has been first solved by using infinite series method, and the formula of the buckling critical loads has been obtained with energy method.
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