Continued fractions

Chain sequence

In the analytic theory of continued fractions, a chain sequence is an infinite sequence {an} of non-negative real numbers chained together with another sequence {gn} of non-negative real numbers by the equations where either (a) 0 ≀ gn < 1, or (b) 0 < gn ≀ 1. Chain sequences arise in the study of the convergence problem – both in connection with the , and also as part of the theory of positive definite continued fractions. The infinite continued fraction of Worpitzky's theorem contains a chain sequence. A closely related theorem shows that converges uniformly on the closed unit disk |z| ≀ 1 if the coefficients {an} are a chain sequence. (Wikipedia).

Video thumbnail

What is the alternate in sign sequence

πŸ‘‰ 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

Video thumbnail

What is a sequence

πŸ‘‰ 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

Video thumbnail

What is the definition of an arithmetic sequence

πŸ‘‰ 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

Video thumbnail

What is the definition of a geometric sequence

πŸ‘‰ 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

Video thumbnail

What is an arithmetic sequence

πŸ‘‰ 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

Video thumbnail

What are the formulas for arithmetic and geometric sequences

πŸ‘‰ 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

Video thumbnail

What is the recursive formula and how do we use it

πŸ‘‰ 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

Video thumbnail

What is the difference between finite and infinite sequences

πŸ‘‰ 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

Video thumbnail

What is the formula for the rule for the nth term of a arithmetic sequence

πŸ‘‰ 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

Video thumbnail

Sequences, On-Sequences and Clips | Algebraic Calculus One | Wild Egg

What exactly is a sequence? In this video we introduce a precise understanding of this important concept, and then also venture towards "on-going" or "boundless" or "infinite" sequences. We also introduce the idea of a "clip" of a sequence, which is a partial representation of a sequence

From playlist Algebraic Calculus One from Wild Egg

Video thumbnail

Biological Sciences M121. Immunology with Hematology. Lecture 07. Antibody Structure & B-Cells.

UCI BioSci M121: Immunology with Hematology (Fall 2013) Lec 07. Immunology with Hematology -- Antibody Structure & B-Cells -- View the complete course: http://ocw.uci.edu/courses/biosci_m121_immunology_with_hematology.html Instructor: David A. Fruman, Ph.D. License: Creative Commons CC-BY

From playlist Biological Sciences M121: Immunology with Hematology

Video thumbnail

Protein evolution (Lecture - 01) by Lucy Colwell

Winter School on Quantitative Systems Biology DATE:04 December 2017 to 22 December 2017 VENUE:Ramanujan Lecture Hall, ICTS, Bengaluru The International Centre for Theoretical Sciences (ICTS) and the Abdus Salam International Centre for Theoretical Physics (ICTP), are organizing a Winter S

From playlist Winter School on Quantitative Systems Biology

Video thumbnail

Stable Homotopy Seminar, 11: Stable Model Categories and Triangulated Categories

(Note: I messed up the first recording and had to re-record the first 20 minutes of this.) I show that cofiber sequences agree with fiber sequences in Spectra, or indeed in any pointed model category where suspension is invertible. The homotopy category of such a model category is a highly

From playlist Stable Homotopy Seminar

Video thumbnail

DeepMind's AlphaFold 2 Explained! AI Breakthrough in Protein Folding! What we know (& what we don't)

#deepmind #biology #ai This is Biology's AlexNet moment! DeepMind solves a 50-year old problem in Protein Folding Prediction. AlphaFold 2 improves over DeepMind's 2018 AlphaFold system with a new architecture and massively outperforms all competition. In this Video, we take a look at how

From playlist Papers Explained

Video thumbnail

Charles Weibel: K-theory of algebraic varieties (Lecture 2)

The lecture was held within the framework of the Hausdorff Trimester Program: K-Theory and Related Fields. Charles Weibel: K theory of algebraic varieties Abstract: Lecture 1 will present definitions for the Waldhausen K-theory of rings, varieties, additive and exact categories, and dg c

From playlist HIM Lectures: Trimester Program "K-Theory and Related Fields"

Video thumbnail

Arthur Mallay Lesk, The architecture of proteins - 8 maggio 2019

https://www.sns.it/it/evento/the-architecture-of-proteins Colloquio della Classe di Scienze Arthur Mallay Lesk (Penn State University) The architecture of proteins Abstract Proteins present us with a great variety of three-dimensional structures, selected to adopt unique folding patter

From playlist Colloqui della Classe di Scienze

Video thumbnail

30. Immunology 1 – Diversity, Specificity, & B cells

MIT 7.016 Introductory Biology, Fall 2018 Instructor: Adam Martin View the complete course: https://ocw.mit.edu/7-016F18 YouTube Playlist: https://www.youtube.com/playlist?list=PLUl4u3cNGP63LmSVIVzy584-ZbjbJ-Y63 Professor Martin introduces the topic of immunity, defined as resistance to d

From playlist MIT 7.016 Introductory Biology, Fall 2018

Video thumbnail

Álvaro Torras Casas (8/5/20): The Persistence Mayer-Vietoris spectral sequence

Title: The Persistence Mayer Vietoris spectral sequence Abstract: In this talk, I will give a brief introduction to the persistent Mayer-Vietoris spectral sequence. The original motivation for studying this object comes from the need to parallelize persistent homology computations. The st

From playlist AATRN 2020

Video thumbnail

Finding the rule of the sequence using multiplication and addition

πŸ‘‰ Learn how to write the explicit formula for the nth term of an arithmetic sequence. 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. An arithmetic sequence is a sequence in which each term of the sequence

From playlist Sequences

Related pages

Complex analysis | Generalized continued fraction | Convergence problem | Quadratic form