大家知道,級数斂散性的判別方法很多,其中最常用的是达朗貝尔法和柯西法。然而很多級数此二法不能判断,而用其他較細致的方法却往往伴随有复杂的計算,p-級数就是一个例子。因而想到:如果有一个較簡捷的方法能判断它,似乎就能弥补达朗貝尔法的不足之处。因为达朗貝尔法只能判断与等比級数斂散速度相同的級数,而p-級数收斂(或发散)則慢得多。于是对p-級数进行了分析,发現它的項是单調递减的,且有 As we all know, there are many methods for judging the convergence of series, of which the most commonly used are the D’Alembert’s method and Cauchy’s method. However, many of these two methods cannot be judged, but using other more detailed methods are often accompanied by complicated calculations. The p-series is an example. So think of: If there is a simpler way to judge it, it seems to be able to make up for the deficiencies of the D’Alembert method. Because the D’Alembert’s method can only judge the series with the same speed of convergence and convergence, the p-series convergence (or divergence) is much slower. So we analyzed the p-series and found that its terms are monotonically decreasing and there are