Dave4Math / Courses / Sequences, Series, and Probability

Sequences, Series, and Probability

Master sequences, series, and probability with these lessons. Learn partial sums, mathematical induction, and the basics of probability. In this course, you'll become adept with sequences and series. The basics of probability is a must!


January 11, 2021

Created by Dave

This course begins Summer 2021.
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Let’s take a journey together. Let’s walk down a road where you’re exploring new mathematical ideas everyday. These ideas are revolutionary and have come at the cost of hundreds of years of precious thinking. Introducing Dave’s online math courses: Sequences, Series, and Probability. In this course, Dave teaches, by example, that success is a journey, not a destination.

Who This Course is For

  • Students in college who want to learn more mathematics.
  • Anyone interested in sequences, series, and probability.
  • Students who are enrolled in precalculus and want to improve their grade.
  • Anyone interested in getting prepared for calculus 1.
  • Anyone wanting to learn about sequences, series, partial sums, mathematical induction, counting principles, and probability.


There is no required textbook, though you will need an up-to-date web browser, paper, and pen. A hand-held scientific calculator of your choice is required.

What You’ll Learn in Sequences, Series, and Probability

  • Sequences
  • Factorial Notation
  • Summation Notation
  • Series
  • Applications
  • Arithmetic Sequences
  • The Sum of a Finite Arithmetic Sequence
  • Geometric Sequences
  • The Sum of a Finite Geometric Sequence
  • Geometric Series
  • Mathematical Induction
  • Sums of Powers of Integers
  • Finite Differences
  • Binomial Coefficients
  • Binomial Expansions
  • Pascal’s Triangle
  • Simple Counting Problems
  • The Fundamental Counting Principle
  • Permutations
  • Combinations
  • The Probability of an Event
  • Mutually Exclusive Events
  • Independent Events
  • The Complement of an Event

Course Description

I recommend the prerequisite course Linear Systems and Matrices. If you’re not sure if this course is for you, checkout the course contents below or find out more by checking out my free precalculus articles.

Course Content

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David A. Smith

Mathematics Educator

I sincerely believe that the potential in every student can be unlocked. As an accomplished and dedicated instructor, I have firm confidence that I can provide significant value to your studies.

I relish teaching and use it as a channel for my creativity as I seek to deliver real-life and relevant connections between the mathematics that I teach and my students. Promoting an active learning environment and excitement about mathematics is my dream come true.

David Smith (Dave) has a B.S. and M.S. in Mathematics and has enjoyed teaching precalculus, calculus, linear algebra, and number theory at both the junior college and university levels for over 20 years. David is the founder and CEO of Dave4Math.