CAJ | 학술논문

将Guass算术几何平均数列和算术调和平均数列两个递推数列进行综合,对具有特殊形式的数列作了一般性的推广,提出三元平均递推数列,利用单调有界定理判断递推数列收敛性.利用函数单调性对递推数列的单调性进行讨论,给出递推数列收敛性的条件,并对此数列的单调性和极限值进行研究.应用单调有界定理证明其极限的存在,并给出该方法在求递推数列极限问题中的一些应用,从而得到两条性质.并对此数列的极限值给予直观阐述.
장Guass산술궤하평균수렬화산술조화평균수렬량개체추수렬진행종합,대구유특수형식적수렬작료일반성적추엄,제출삼원평균체추수렬,이용단조유계정리판단체추수렬수렴성.이용함수단조성대체추수렬적단조성진행토론,급출체추수렬수렴성적조건,병대차수렬적단조성화겁한치진행연구.응용단조유계정리증명기겁한적존재,병급출해방법재구체추수렬겁한문제중적일사응용,종이득도량조성질.병대차수렬적겁한치급여직관천술.
The Guass arithmetic geometric mean sequence and arithmetic harmonic mean sequence was synthesized. We have got the general promotion of the sequence of special form. Ternary average recur-rence sequence is put forward. The monotone bounded theorem is used to determine the convergence of recurrence sequence. Judging the monotonicity of recurrence sequence was the key. The monotonicity of recurrence sequence was discussed by using the monotonicity of the function. The convergence conditions of recursive sequence are given,and the conclusion of its convergence is obtained. The result indicates that application of monotone bounded theorem shows the existence of the limit. The method is useful to find the limit of some tierative sequences. In order to get the two properties, limit values of this recurrence sequence of monotonicity are studied.