Sequences and Series - Complete Calculus and Precalculus Course

Math with Professor V via YouTube

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Provider

YouTube
Pricing

Free Video
Languages

English
Duration & workload

1 day 6 hours 32 minutes
Sessions

On-Demand
Level

Intermediate

Found in

Master sequences and series through this comprehensive video course covering fundamental concepts from precalculus through advanced calculus topics. Begin with sigma notation review and progress through sequences, geometric sequences, and series fundamentals. Explore convergence and divergence of infinite sequences, including monotonic and bounded sequences, and apply the ratio test for sequences. Dive deep into infinite series analysis using multiple convergence tests including the integral test, comparison tests, limit comparison test, alternating series test, ratio test, and root test. Learn to work with telescoping series, understand absolute versus conditional convergence, and develop strategic approaches for determining which convergence test to apply. Study power series representations of functions, including finding radius and interval of convergence, differentiation and integration of power series. Master Taylor and Maclaurin series construction and applications, including binomial series and using series to evaluate limits. Practice error approximation with Taylor polynomials and Taylor's inequality. Apply knowledge through extensive problem-solving sessions including 100 practice questions, exam walkthroughs, and daily series challenges that demonstrate real-world application of convergence tests and series manipulation techniques.

Syllabus

Review of Sigma Notation (for the Calculus Student) | Math with Professor V
Precalculus: Sequences and Series (Section 12.1) | Math with Professor V
Precalculus: Geometric Sequences and Series (Section 12.3) | Math with Professor V
Calculus 2: Sequences (Section 11.1) | Math with Professor V
Monotonic and Bounded Sequences | Calculus 2 | Math with Professor V
The Ratio Test for Sequences | Calculus 2 | Math with Professor V
Infinite Sequences - Convergent or Divergent? | Calculus 2 | Math with Professor V
Infinite Sequences PART 2- Convergent or Divergent? | Calculus 2 | Math with Professor V
Calculus 2: Series (Section 11.2) | Math with Professor V
Telescoping Series/Telescoping Sums for Calculus 2 | Math with Professor V
Calculus 2: The Integral Test (Section 11.3) | Math with Professor V
Calculus 2: Comparison Tests (Section 11.4) | Math with Professor V
Calculus 2: The Comparison and Limit Comparison Tests (Part 2) | Math with Professor V
Calculus 2: Alternating Series (Section 11.5) | Math with Professor V
Factorials! What Are They? How to Simplify? | Math with Professor V
Calculus 2: Absolute Convergence and the Ratio and Root Tests (Section 11.6) | Math with Professor V
Testing for Absolute & Conditional Convergence | Easy Explanation! | Math with Professor V
Calculus 2: The Ratio Test - Part 2 | Math with Professor V
Calculus 2: The Root Test Part 2 | Math with Professor V
Calculus 2: Strategy for Testing Series (Section 11.7) | Math with Professor V
Strategy for Testing Series | Solving Problems Calculus 2 | Math with Professor V
Calculus 2: Power Series (Section 11.8) | Math with Professor V
Calculus 2: Representations of Functions as Power Series Part 1 (Section 11.9) | Math w Professor V
Calculus 2: Differentiation and Integration of Power Series-Pt 2 (Section 11.9) | Math w Professor V
Power Series - Made Easy! | Power Series Representation of a Function | Math with Professor V
Finding the Radius & Interval of Convergence for Power Series! | Calculus 2 | Math with Professor V
Calculus 2: Taylor and Maclaurin Series (Part 1) | Math with Professor V
Calculus 2: Taylor & Maclaurin Series Part 2/Binomial Series (Section 11.10) | Math with Professor V
Finding Taylor and Maclaurin Series for Functions (Calculus 2) | Math with Professor V
Using Series to Evaluate Limits | 3-Step Easy Process! | Calculus 2 | Math with Professor V
Calculus 2: Applications of Taylor Polynomials (Section 11.11) | Math with Professor V
Series of the Day 7.12.24 | Special Channel Member Request! | Math with Professor V
Series of the Day 7.19.24 | Does It Converge or Diverge??? | Math with Professor V
Series of the Day 7.24.24 | Does it Converge or Diverge?! | Which test to use? Math with Professor V
Calculus 2: Solving Exam 3 -All things SEQUENCES & SERIES! -Fall 2019 Part 1| Math with Professor V
Calculus 2: Solving Exam 3 -All things SEQUENCES & SERIES! -Fall 2019 Part 2| Math with Professor V
The Limit Comparison Test: How & When To Use It | Sequences & Series | Math with Professor V
The Ratio and Root Tests for Infinite Series - When To Use Them & How - Math with Professor V
Solving 100 QUESTIONS on all things SEQUENCES & SERIES! - PART 1 | Math with Professor V
Solving 100 QUESTIONS on all things SEQUENCES & SERIES! - PART 2 | Math with Professor V
Approximating Error for Taylor Polynomials | Taylor's Inequality | Math with Professor V
The Integral Test for Infinite Series: Step by Step Explanation! | Math with Professor V
Series of the Day 10.30.25 | Which Convergence Test Do You Use?!
Stop Mixing These Up! Absolute vs Conditional Convergence Explained (Calc 2)
Series of the Day 11.3.25 | Using the Root Test + L’Hôpital’s Rule (Don’t Skip This Step!)
Series of the Day 11.8.25 | The Trick to Picking the Right Series Test (Limit Comparison Secrets)
Series Test Strategy (Calc 2 / AP Calc BC) | Which One Do You Use?
Calculus 2 Exam 3 (Spring 2025) Part 2: Ratio Test, Power Series, Taylor Series & Convergence
Calculus 2 Exam 3 Walkthrough Fall 2025: Sequences & Series Review (Fast Breakdown)