Linear algebra | Integer sequences | Dynamical systems | Combinatorics | Recurrence relations
In mathematics and theoretical computer science, a constant-recursive sequence is an infinite sequence of numbers where each number in the sequence is equal to a fixed linear combination of one or more of its immediate predecessors. A constant-recursive sequence is also known as a linear recurrence sequence, linear-recursive sequence, linear-recurrent sequence, a C-finite sequence, or a solution to a linear recurrence with constant coefficients. The most famous example of a constant-recursive sequence is the Fibonacci sequence , in which each number is the sum of the previous two. The power of two sequence is also constant-recursive because each number is the sum of twice the previous number. The square number sequence is also constant-recursive. However, not all sequences are constant-recursive; for example, the factorial number sequence is not constant-recursive. All arithmetic progressions, all geometric progressions, and all polynomials are constant-recursive. Formally, a sequence of numbers is constant-recursive if it satisfies a recurrence relation where are constants. For example, the Fibonacci sequence satisfies the recurrence relation where is the th Fibonacci number. Constant-recursive sequences are studied in combinatorics and the theory of finite differences. They also arise in algebraic number theory, due to the relation of the sequence to the roots of a polynomial; in the analysis of algorithms as the running time of simple recursive functions; and in formal language theory, where they count strings up to a given length in a regular language. Constant-recursive sequences are closed under important mathematical operations such as term-wise addition, term-wise multiplication, and Cauchy product. The Skolem–Mahler–Lech theorem states that the zeros of a constant-recursive sequence have a regularly repeating (eventually periodic) form. On the other hand, the Skolem problem, which asks for algorithm to determine whether a linear recurrence has at least one zero, is a famous unsolved problem in mathematics. (Wikipedia).
Applying the recursive formula to a sequence to determine the first five terms
👉 Learn all about recursive sequences. Recursive form is a way of expressing sequences apart from the explicit form. In the recursive form of defining sequences, each term of a sequence is expressed in terms of the preceding term unlike in the explicit form where each term is expressed in
From playlist Sequences
Using the recursive formula to find the first four terms of a sequence
👉 Learn all about recursive sequences. Recursive form is a way of expressing sequences apart from the explicit form. In the recursive form of defining sequences, each term of a sequence is expressed in terms of the preceding term unlike in the explicit form where each term is expressed in
From playlist Sequences
What is the recursive formula and how do we use it
👉 Learn about sequences. A sequence is a list of numbers/values exhibiting a defined pattern. A number/value in a sequence is called a term of the sequence. There are many types of sequence, among which are: arithmetic and geometric sequence. An arithmetic sequence is a sequence in which
From playlist Sequences
Learn how to find the first five terms of a sequence using the recursive formula
👉 Learn all about recursive sequences. Recursive form is a way of expressing sequences apart from the explicit form. In the recursive form of defining sequences, each term of a sequence is expressed in terms of the preceding term unlike in the explicit form where each term is expressed in
From playlist Sequences
Applying the recursive formula to a geometric sequence
👉 Learn all about recursive sequences. Recursive form is a way of expressing sequences apart from the explicit form. In the recursive form of defining sequences, each term of a sequence is expressed in terms of the preceding term unlike in the explicit form where each term is expressed in
From playlist Sequences
How to find the first four terms of a recursive formula
👉 Learn all about recursive sequences. Recursive form is a way of expressing sequences apart from the explicit form. In the recursive form of defining sequences, each term of a sequence is expressed in terms of the preceding term unlike in the explicit form where each term is expressed in
From playlist Sequences
Sequences: Introduction to Solving Recurrence Relations
This video introduces solving recurrence relations by the methods of inspection, telescoping, and characteristic root technique. mathispower4u.com
From playlist Sequences (Discrete Math)
How to determine the first five terms for a recursive sequence
👉 Learn all about recursive sequences. Recursive form is a way of expressing sequences apart from the explicit form. In the recursive form of defining sequences, each term of a sequence is expressed in terms of the preceding term unlike in the explicit form where each term is expressed in
From playlist Sequences
Determine Recursive Formulas for Sequences
This video explains how to find recursive formulas for a sequence. mathispower4u.com
From playlist Sequences (Discrete Math)
Arithmetic and Geometric Sequences | Explanation + Examples | Precalculus
This video is an introduction to sequences, where I focus on arithmetic and geometric sequences. Timestamps: What is a sequence? 00:34 Explicit vs recursive definitions: 3:10 What is an arithmetic sequence? 5:09 General formulas for arithmetic sequences: 7:39 Arithmetic sequence example
From playlist Precalculus
MIT 6.006 Introduction to Algorithms, Spring 2020 Instructor: Jason Ku View the complete course: https://ocw.mit.edu/6-006S20 YouTube Playlist: https://www.youtube.com/playlist?list=PLUl4u3cNGP63EdVPNLG3ToM6LaEUuStEY This session focuses on preparing for the quiz. High-level concepts are
From playlist MIT 6.006 Introduction to Algorithms, Spring 2020
15. Dynamic Programming, Part 1: SRTBOT, Fib, DAGs, Bowling
MIT 6.006 Introduction to Algorithms, Spring 2020 Instructor: Erik Demaine View the complete course: https://ocw.mit.edu/6-006S20 YouTube Playlist: https://www.youtube.com/playlist?list=PLUl4u3cNGP63EdVPNLG3ToM6LaEUuStEY This is the first of four lectures on dynamic programing. This begin
From playlist MIT 6.006 Introduction to Algorithms, Spring 2020
Taylor polynomials -- Calculus II
This lecture is on Calculus II. It follows Part II of the book Calculus Illustrated by Peter Saveliev. The text of the book can be found at http://calculus123.com.
From playlist Calculus II
Arithmetic Sequences and their Sums [Discrete Math Class]
This video is not like my normal uploads. This is a supplemental video from one of my courses that I made in case students had to quarantine. In this video, we define and investigate arithmetic sequences. We see how to find both recursive formulas and closed formulas for arithmetic sequenc
From playlist Finite Sums
Alp Bassa: Good Recursive Towers
Curves over finite fields of large genus with many rational points have been of interest for both theoretical reasons and for applications. In the past, various methods have been employed for the construction of such curves. One such method is by means of explicit recursive equations and w
From playlist Algebraic and Complex Geometry
CSE 373 -- Lecture 20, Fall 2020
From playlist CSE 373 -- Fall 2020
MIT 6.006 Introduction to Algorithms, Spring 2020 Instructor: Jason Ku View the complete course: https://ocw.mit.edu/6-006S20 YouTube Playlist: https://www.youtube.com/playlist?list=PLUl4u3cNGP63EdVPNLG3ToM6LaEUuStEY This session focuses on preparing for the quiz. High-level concepts are
From playlist MIT 6.006 Introduction to Algorithms, Spring 2020
Lecture 21 | Programming Paradigms (Stanford)
Lecture by Professor Jerry Cain for Programming Paradigms (CS107) in the Stanford University Computer Science department. In this lecture, Prof. Cain continues discussing the functional program and the Scheme programming language by focusing upon function pointers. Programming Paradigm
From playlist Lecture Collection | Programming Paradigms
How to use the recursive formula to evaluate the first five terms
👉 Learn all about recursive sequences. Recursive form is a way of expressing sequences apart from the explicit form. In the recursive form of defining sequences, each term of a sequence is expressed in terms of the preceding term unlike in the explicit form where each term is expressed in
From playlist Sequences
Foundations - Seminar 12 - Gödel's incompleteness theorem Part 4
Billy Price and Will Troiani present a series of seminars on foundations of mathematics. In this seminar Will Troiani continues with the proof of Gödel's incompleteness theorem, by proving that general recursive functions are representable. You can join this seminar from anywhere, on any
From playlist Foundations seminar