우리나라 有料老人福祉施設의 活性化 方案에 관한 硏究

다국어 초록 (Multilingual Abstract)

This study shows the contents of "the limit of Sequences" and "Convergence and Divergence of Series" in the highschool mathematics curriculum. First of all, I mainly analyze how teachers deal with "the limit of Sequences" and "Convergence and Divergence of Series" and point out the problems followed.
For the solving method of the problems appearing in teaching them in high school, I examine and explain exactly the conception of the limit of Sequences with introduction of ε-δ method and extend it to the Series related to it.
Summarizing the main contents :
1) In the Sequence {a(n)}, "Sequence {a(n)} converges to α" means "given ε>0, there is a natural number N such that |a(n)-α|<ε holds for all n≥N". This concept is more logical and exact than the direct definition of □a(n)=α. In this time, α is called the limit of the Sequence {a(n)}.
2) Of the tests of Convergence and Divergence of Sequence, there are usually monotone convergence therem and Cauchy test, but the one is only used in the monotone Sequence. On the other hand the Cauchy test is not influenced by monotone Sequence and we had better ignore the limit as well.
3) There are many kinds of tests of Convergence and Divergence about the infinite series □a(n).
They are different according to the kinds of series. In general, the tests that we have used are Integral Test, Comparative Test, Ratio test, Root Test, Limit Comparison Test, and Alternating Series Test. Finally the result of this study, I hope, can give more or less help to you in teaching the Sequences and Series.

목차 (Table of Contents)

• 目次
• I. 서론 = 1
• II. 수열의 극한의 기초 개념 = 3
• A. 유계성 = 3
• B. 상한, 하한 = 4
• C. 집적점 = 7
• III. 수열의 극한 = 10
• A. 수열의 정의 = 10
• B. 수열의 극한의 정의 = 10
• 1. 현행 교육과정 분석 및 문제점 = 10
• 2. 극한의 정의 = 13
• C. 수열의 극한에 관한 정리 = 15
• D. 수열의 수렴 발산 판정법 = 21
• 1. 단조수렴 정리 = 21
• 2. Cauchy 판정법 = 23
• IV. 급수 = 27
• A. 급수의 수렴 발산의 정리 = 27
• B. 급수에 관한 정리 = 28
• C. 여러가지 급수 = 30
• D. 급수의 수렴 발산 판정법 = 35
• V. 결론 = 41
• 참고문헌 = 45
• 영문초록 = 46