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Sequences and Summations

Sequences and Summations

Sequences and Summations. Section 2.4. Section Summary. Sequences. Examples: Geometric Progression, Arithmetic Progression Recurrence Relations Example: Fibonacci Sequence Summations. Introduction. Sequences are ordered lists of elements. 1, 2, 3, 5, 8 1, 3, 9, 27, 81, ��.

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7.2 Solving Recurrence Relations

7.2 Solving Recurrence Relations

7.2 Solving Recurrence Relations. Definition 1 (p. 460)- LHRR-K. Def: A linear homogeneous recurrence relations of degree k with constant coefficients (referred to as � LHRR-K �) is a recurrence relation of the form

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Solving Recurrence Relations

Solving Recurrence Relations

Solving Recurrence Relations. So what does T(n) = T(n-1) +n look like anyway?. Recurrence Relations. Can easily describe the runtime of recursive algorithms Can then be expressed in a closed form (not defined in terms of itself) Consider the linear search:. Eg. 1 - Linear Search.

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Solving Recurrence Relations

Solving Recurrence Relations

Solving Recurrence Relations. So what does T(n) = T(n-1) +n look like anyway?. Recurrence Relations. Can easily describe the runtime of recursive algorithms Can then be expressed in a closed form (not defined in terms of itself) Consider the linear search:. Eg. 1 - Linear Search.

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391 views • 19 slides
Lecture 17

Lecture 17

Lecture 17. Generating Functions. Recap. Generating functions are defined by a sequence as follows:. Thus: For every sequence there a generating function and for every sequence there is a generating function. Idea: Use properties of functions to solve problems about sequences.

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Chapter 8

Chapter 8

Chapter 8. Recursion. 8.2. Solving Recurrence Relations by Iteration. Recursion. A Sequence can be defined as: informally be providing a few terms to demonstrate the pattern, i.e. 3, 5, 7, �. give an explicit formula for it nth term, i.e.

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Discrete Structures

Discrete Structures

Discrete Structures. Chapter 5: Sequences, Mathematical Induction, and Recursion 5.7 Solving Recurrence Relations by Iteration. The keener one�s sense of logical deduction, the less often one makes hard and fast inferences. � Bertrand Russell, 1872 � 1970 . Method of Iteration.

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