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The document discusses linear recurrence relations, arithmetic sequences, and geometric sequences. It provides examples of how to write recurrence relations for various situations involving increasing or decreasing patterns over time. Examples are given of how to calculate individual terms and find a formula to represent the entire sequence. Key aspects covered include writing recurrence relations, finding subsequent terms, deriving formulas, and applying the concepts to word problems involving patterns of change over time.Reccurrence relations
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This document provides information about recurrence relations and their applications in higher mathematics. It begins by introducing different types of sequences and exploring whether they can be described by a formula or recurrence relation. It then discusses linear recurrence relations and how they can model growth and decay scenarios. The document also covers divergence and convergence of sequences, and provides examples of applying recurrence relations to problems involving populations, waste disposal, medication in hospitals, and other scenarios.CPSC 125 Ch 2 Sec 5
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This document discusses properties and solving techniques for recurrence relations. It covers linear vs nonlinear relations, homogeneous vs inhomogeneous relations, and the order of relations. It also describes the expand, guess, verify technique and using solution formulas to solve recurrence relations in closed form. Examples are provided for each concept.CPSC 125 Ch 3 Sec 4 6
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The document discusses permutations and combinations. Some key points:
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A recurrence relation defines a sequence based on a rule that gives the next term as a function of previous terms. There are three main methods to solve recurrence relations: 1) repeated substitution, 2) recursion trees, and 3) the master method. Repeated substitution repeatedly substitutes the recursive function into itself until it is reduced to a non-recursive form. Recursion trees show the successive expansions of a recurrence using a tree structure. The master method provides rules to determine the time complexity of divide and conquer recurrences.
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ABC Talk #10 麹伎 覃覈襴 覿螻 蟯襴
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- 1. (Recurrence Relation) り ohgyun@gmail.com
- 2. sequence progression 企 蠏豺 磯 谿襦襦 危 : 1, 2, 3, 4 轟 襦 : 覓語,
- 3. 煙姶 arithmetic sequence 谿螳 殊 : 1, 3, 5, 7, 9, 谿 = 螻旧姶(common difference)
- 4. recurrence relation ( formula) 伎 伎 焔渚 蟯螻 蠍 伎 螻 轟 螳朱
- 5. 煙姶伎 朱
- 6. 焔 geometric sequence 螳 殊 觜襯 螳讌 : 2, 4, 8, 16, ... 觜 = 螻給(common ratio)
- 7. 焔伎 朱
- 8. permutation 襦 るジ n螳 譴 r螳(n>=r)襯 譴襦 語磯 蟆曙一
- 9. 伎 朱
- 10. 譟壱 Combination 危螻(binomial coefficient)手 n螳 讌 r螳 覿覿讌 螻襯企 譟 n螳 襦 るジ 覓手唄 譴 r螳襯 觸 蟆曙一 n螳 襦 るジ 覓手唄 譴 n-r螳襯 觸 蟆螻朱 螳
- 11. 譟壱 蠏 轟:
- 12. 譟壱 朱 願骸 襷谿螳讌襦 螻壱 :
- 13. 譴覲 repeated permutation n螳 襦 るジ 譴 譴覲旧 r螳襯 觸 危 蟆 : 1~4 一 4螳襦 襷 語襴 4^3 = 64
- 14. circular permutation n螳襯 朱 危 蟆曙一 蠍 覓語 n螳螳 譴覲給
- 15. 殊殊 n螳 襦 るジ 譬襯 蟲襦 覈蟇語企ゼ 襷 蟆曙一 願骸 觜訣讌襷 覈蟇語企 れ企 螳 蟆朱 豬蠍覩襦 2覦郁 譴覲給
- 16. 譴覲旧＾ repeated combination 譯殊伎 讌 譴 觸 狩 譴覲旧 觸企 蟆