作 者: ;
机构地区: 广东商学院
出 处: 《四川师范大学学报(自然科学版)》 2004年第3期245-247,共3页
摘 要: 利用偶数项、奇数项与一般项的关系 :a2n ≤pan,a2n+ 1≤qan+ 1(p +q<1)和a2n≥pan,a2n+ 1≥qan+ 1(p,q>0 ,p +q≥ 1) ,给出了正项级数一个简捷而又较常规方法更为精细的敛散性判别法 ,它是一个全新的定理 ,有广泛的适用性 . A new theorem on convergence of positive serieses is proved by using the relations:a_(2n)≤pa_n,a_(2n+1)≤qa_(n+1)(p+q<1) and a_(2n)≥pa_n,a_(2n+1)≥qa_(n+1)(p,q>0,p+q≥1). It is simpler, and more precise than common methods, and it is suitable for many circumstances.