
Dear student, welcome to this introductory lecture on sequences and series. In this lecture, I will briefly introduce the concept of sequences and series, together with a few examples for illustration. Please download the notes before viewing the lecture. Thank you! Cheers! ;-)
Dear student, welcome to this lecture. In this lecture, I will introduce the arithmetic sequences, in particular, the general nth term expression. Please remember to download the notes before viewing the lecture video. Cheers! ;-)
Hi everyone. Welcome to this lecture. In this lecture, I will introduce the arithmetic sum of an arithmetic sequence. Please download the notes before viewing the lecture. In addition, for students who are interested to know about the proof for the Arithmetic Sum formula, I have attached the proof in this lecture as an additional resource for your reading. Thank you! Cheers! ;-)
Hi everyone. Welcome to this lecture. In this lecture, I will introduce the concept of the general nth term of the geometric sequence. PLease download the lecture notes before viewing the video lecture. Thank you! ;-)
Dear student, welcome to this lecture on Geometric Sum. Please remember to download the notes before viewing the lecture video. In addition, for students who are interested to know the proof for the Geometric Sum formula, I have attached the proof in this lecture as an additional resource for your reading. Thank you! ;-)
Hi everyone. Welcome to this lecture. In this lecture, I will introduce the Geometric Sum to Inifinity. Please remember to download the lecture notes before viewing the lecture video. Cheers! ;-)
Hi everyone. Welcome to this lecture. In this lecture, I will discuss the solution to the Practice 1 problem. You are strongly encouraged to try the question before viewing the video solution. Thank you! ;-)
Hi everyone. Welcome to this lecture. In this lecture, I will discuss the solution to the Practice 2 problem. You are strongly encouraged to try the question before viewing the video solution. Thank you! ;-)
Hi everyone. Welcome to this lecture. In this lecture, I will introduce the sigma notation summation sign. Please download the notes before viewing the lecture video. Thank you! ;-)
Hi everyone, welcome to this lecture. In this lecture, I will introduce several standard results for summation. Please download the notes before viewing the lecture video. Thank you! Cheer! :-)
Dear student, welcome to this lecture. In this lecture, I will introduce the AP and GP summation methods. Please download the notes before viewing the lecture video. Cheers! :-)
Hi everyone. Welcome to this lecture. In this lecture, I will discuss about recurrence relations and connection with summation of series. Please remember to download the notes before viewing the video lecture. Cheers! :-)
Dear student, welcome to this lecture. In this video lecture, I will introduce the basic concept of the Method of Difference as a summation technique. Please remember to download the notes before viewing the lecture video. Please enjoy the lesson! Cheers! :-)
Dear student. Welcome to this practice 3 lecture. In this lecture, I will present a problem involving recurrence relations and summation series. You are strongly encouraged to download and attempt the problem before viewing the solution video. Thank you! :-)
Dear student, welcome to this practice 4 solution video. The problem presented in this lecture is a question about the method of difference. You are strongly encouraged to try the problem before viewing the solution video. Thank you! :-)
Dear student, welcome to this lecture. In this lecture, I shall introduce a well-known expansion series called the Taylor Series. Please remember to download the student notes before viewing the lecture. Thank you! :-)
Hi everyone. Welcome to this lecture. In this lecture, I will introduce the concept of the radius of convergence as well as the ratio test. Please remember to download the notes before viewing the lecture video. Cheers! :-)
Dear student, welcome to this lecture. In this lecture, I shall discuss the solutions to two practice examples of Taylor Series. You are strongly encouraged to try the questions before viewing the solution video. Thank you! :-)
HI everyone. Welcome to this lecture. In this lecture, I shall introduce the Binomial series and expansion, particularly on the various definitions, notations as well as the Binomial Coefficient. You are strongly encouraged to download the notes before viewing the lecture video. Cheers! :-)
Dear student, welcome to this Binomial Series and Expansion lecture. In this lecture, I shall introduce the binomial series expansion for positive integer power of n. Please remember to download the notes before viewing the lecture video. Enjoy the lecture. Thank you! :-)
Dear student, welcome to this lecture. In this lecture, I shall discuss the Binomial Expansion of Fractional or Negative Integer power of n. Please remember to download the notes before viewing the lecture video. Enjoy the lesson! Cheers! :-)
Dear student, welcome to this lecture on Binomial series expansion. In this lecture, I will discuss about the validity range of x in a typical binomial series expansion of (1 + x) to the power of n. Please remember to download the notes before viewing the lecture. Enjoy the video! Cheers! :-)
Dear student, welcome to this lecture. In this lecture, I will discuss about the binomial series expansion for descending power of x. Please rememeber to download the notes before viewing the lecture video. Enjoy the lecture! Cheers! :-)
Dear student, welcome to this lecture. In this lecture, I shall discuss the solution to a practice tutorial problem. You are strongly encouraged to attempt the problem before viewing the solution video. Cheers! :-)
Dear student, welcome to this lecture. In this lecture, I will introduce an important and popular expansion series called the Maclaurin's series expansion. Please remember to download the notes before viewing the lecture video. Enjoy the lecture! Cheers! :-)
Dear student, welcome to this lecture on Maclaurin's series. In this lecture, I will introduce several standard expansion series for use to obtain other similar expansion series. Please remember to download the notes before viewing the lecture video. Enjoy the lecture! Cheers! :-)
Dear student, welcome to this Maclaurin's series expansion lecture. In this lecture, I will introduce three main types of question structures for Maclaurin's series questions. Please remember to download the notes before viewing the lecture. Hope you enjoy the lecture! Cheers! :-)
Dear student, welcome to this lecture. In this lecture, I shall introduce an application of the Maclaurin's series - the small angle approximation. Please remember to download the notes before viewing the lecture video. Enjoy the lecture! Cheers! :-)
Dear student, welcome to this problem-solving lecture on Maclaurin's series expansion. In this lecture, I shall discuss the solution to a practice problem. You are strongly encouraged to try and solve the problem before viewing the lecture video. Cheers! :-)
Dear student, welcome to this lecture. In this lecture, I will do an introduction to the Fourier Series expansion. You are strongly encouraged to download the notes and refer to them during the viewing of the lecture video for optimal learning experienece. Thank you! :-)
In this lecture, I will present a problem in summation and to solve using the Method-of-Difference. You are strongly encouraged to try the problem on your own before viewing the solution video. Cheers! :-)
Dear students,
Welcome to this course on "Master the Fundamentals of Sequences and Series"!
This course is designed specially for students who are: doing college-level mathematics, taking their IGCSE/GCE A level or the IB SL/HL Math examinations.
At the end of the course, and depending on which exams you are taking, you will learn most/all of the following:
concepts of sequences and series
arithmetic sequences and series (the arithmetic term and the sum)
geometric sequences and series (the geometric term and the sum)
Sum to Infinity
The summation sign (sigma notation)
Method of Difference
Binomial Series - concepts and applications
expansion for integer powers and fractional powers
Taylor's Series - concepts and applications
Maclaurin's Series - concepts and applications
Small angle approximations using Maclaurin's Series
Fourier Series introduction
Along the way, there will be ample practice questions for you to get familiarized with the various concepts of sequences and series. You will also learn how to apply the concepts to solve problems.
If you encounter any issues with the course, please do not hesitate to contact me for more clarifications.
I hope that you will find this course useful in your academic pursuit. Enjoy the course! Cheers!
Dr Ling M K Daniel, PhD
oo oo oo oo oo oo oo oo oo oo oo oo oo oo oo oo oo oo oo oo oo oo oo oo oo oo oo