Articles containing proofs | Sequences and series | Arithmetic series
An arithmetic progression or arithmetic sequence (AP) is a sequence of numbers such that the difference between the consecutive terms is constant. For instance, the sequence 5, 7, 9, 11, 13, 15, . . . is an arithmetic progression with a common difference of 2. If the initial term of an arithmetic progression is and the common difference of successive members is , then the -th term of the sequence is given by: , If there are m terms in the AP, then represents the last term which is given by: . A finite portion of an arithmetic progression is called a finite arithmetic progression and sometimes just called an arithmetic progression. The sum of a finite arithmetic progression is called an arithmetic series. (Wikipedia).
Intro to Geometric Progressions (1 of 3: Definitions)
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What is an arithmetic progression? - Week 1 - Lecture 5 - Sequences and Series
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From playlist Ohio State: Calculus Two with Jim Fowler: Sequences and Series | CosmoLearning Mathematics
Support me on Patreon: https://www.patreon.com/mathsaurus Introduction to Arithmetic progressions, including nth term and term to term definitions. Visit http://www.mathsaurus.com/ for more free GCSE and A-level maths videos and resources. Visit the Mathsaurus Amazon shop at https://www.
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Sum of an Arithmetic Progression (2 of 5: Developing & using alternate formula)
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What is an arithmetic sequence
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What is the definition of an arithmetic sequence
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General formula for Arithmetic Progressions
Support me on Patreon: https://www.patreon.com/mathsaurus This video describes the general formulae used to describe arithmetic progressions. Visit http://www.mathsaurus.com/ for more free GCSE and A-level maths videos and resources Visit the Mathsaurus Amazon shop at https://www.amazo
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Tom Sanders - Roth's theorem on arithmetic progressions
Roth's theorem on arithmetic progressions
From playlist 28ème Journées Arithmétiques 2013
Arithmetic regularity, removal, and progressions - Jacob Fox
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From playlist Mathematics
Learn to use summation notation for an arithmetic series to find the sum
👉 Learn how to find the partial sum of an arithmetic series. A series is the sum of the terms of a sequence. An arithmetic series is the sum of the terms of an arithmetic sequence. The formula for the sum of n terms of an arithmetic sequence is given by Sn = n/2 [2a + (n - 1)d], where a is
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Linear equations in smooth numbers - Lilian Matthiesen
Special Year Research Seminar Topic: Linear equations in smooth numbers Speaker: Lilian Matthiesen Affiliation: KTH Royal Institute of Technology Date: October 18, 2022 A number is called y-smooth if all of its prime factors are bounded above by y. The set of y-smooth numbers below x for
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Introduction to additive combinatorics lecture 11.2 --- Part of the proof of Roth's theorem
Roth's theorem, one of the fundamental results of additive combinatorics, states that for every positive δ and every positive integer k there exists a positive integer n such that every subset of {1,2,...,n} of size at least δn contains an arithmetic progression of length 3. (This was late
From playlist Introduction to Additive Combinatorics (Cambridge Part III course)
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Additive Energy of Regular Measures in One and Higher Dimensions, and the Fractal... - Laura Cladek
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The Green - Tao Theorem (Lecture 1) by D. S. Ramana
Program Workshop on Additive Combinatorics ORGANIZERS: S. D. Adhikari and D. S. Ramana DATE: 24 February 2020 to 06 March 2020 VENUE: Madhava Lecture Hall, ICTS Bangalore Additive combinatorics is an active branch of mathematics that interfaces with combinatorics, number theory, ergod
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Christian Elsholtz: Improved cap constructions, and sets withoutarithmetic progressions
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How to find the rule of a arithmetic sequence given two values in the sequence
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The Green-Tao theorem and a relative Szemeredi theorem - Yufei Zhao
Yufei Zhao Massachusetts Institute of Technology March 3, 2014 The celebrated Green-Tao theorem states that there are arbitrarily long arithmetic progressions in the primes. In this talk, I will explain the ideas of the proof and discuss our recent simplifications. One of the main ingredie
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