Sequences And Series: From Theory To Application.

Power Of Patterns: An Exploration Of Sequences And Series.

What you'll learn
Students will learn to derive and apply formulas for the nth term and the sum of finite and infinite arithmetic and geometric series.
He or She will learn to define and identify different types of sequences, such as arithmetic, geometric, and recursive sequences.
Students will practice solving a wide range of problems involving sequences and series, including those related to real-world applications.
They will learn about power series, including finding their interval of convergence and determining the Taylor series generated by a given function.
He or She will be able to identify what type a given sequence or series is and find a formula for the nth term, any required term and the sum.
The Learner will be able to indicate whether a given sequence or series is arithmetic, whether it is finite or infinite, find a formula for the nth term.
The Learner will be able to identify whether a given sequence is geometric, whether it is finite or infinite, find a formula for its nth term.
They will understand the concept of a series as the sum of the terms of a sequence and learn to differentiate between finite and infinite series.
He or She will be able to solve for any term , find the sum of finite and infinite arithmetic and geometric sequence and series.
The Learner can expect to solve for the sum of infinite arithmetic sequence and series by partial sum method.
Plot and identify graphs of arithmetic and geometric sequences and series.
Use factorial method to simplify arithmetic or geometric expressions and equations.
Use summation notation to solve for the sum of finite and infinite geometric sequence and series.
Use summation notation to solve for the sum other type of sequence and series.
He or She will be able to find the common difference of arithmetic progression when the sum of nth terms is given.
The student will be able to conmpare the common ratio of two geometric progressions with equal sum to infinity.
He or She will be able to use sigma notation to write the formular for nth term of a given series.
The student will be able to find the required term, nth term and sum of any sequences and series other than arithmetic and geometric sequences and series.

Requirements
Writing materials: pen , pencil , paper and earphone
Computer, Laptop, Smartphone Or Notepad connected to internet network.
A quite place to help accelerate understanding and follow up.
A chair and a desk, a calculator or four figure table and a mathset.
Elementary knowledge of sequences and series is a plus.

Description
This is an extensive course in sequences and series. You will explore how these fundamental mathematical concepts are used to model real-world phenomena. From the growth of populations to the spread of information, discover how sequences and series can be used to understand and predict patterns in diverse fields. You'll learn to identify, analyze, prove convergence of sequences and series, including infinite geometric series and solve problems involving arithmetic and geometric sequences and series, develop your problem-solving skills, and gain a deeper appreciation for the power of mathematics in everyday life. It is an essential building block for calculus and advanced mathematics. Through interactive lectures and problem-solving sessions, you will develop the ability to construct mathematical arguments and apply the epsilon-delta definition of convergence.As you delve deep into this course, you will learn the world of Fibonacci numbers and the Golden Ratio, examining their presence in nature, art, and mathematics. Students will learn about the history and properties of the Fibonacci sequence, explore its connections to the Golden Ratio, and discover its applications in various fields.       Let us, explicitly, define the constituent of this comprehensive course. It comprises in-depth knowledge of the course: use sequence notation to write terms of a sequence, write a rule for the nth term of a sequence, sum the terms of a sequence to obtain a series and use summation notation, learn about finite and infinite sequences and series, respectively ; use table of values and graphs to illustrate pattern of sequence , identify arithmetic sequences, write a rules for the nth term of arithmetic sequences, solve for a required term when two other terms are given, find partial sum and sums of finite arithmetic sequences using arithmetic progression formula, use sigma notation method to find the sum of arithmetic sequences and series ,use table of values and graphs to illustrate the concept of finite arithmetic sequence, model with arithmetic sequences and series, identify geometric sequences, write rules for geometric sequences, find partial sum and sums of finite geometric sequences using summation notation and to find sums using geometric progression formula, use table of values and graphs to illustrate the relationship between the terms of a given geometric sequence , Solve for the partial sum of infinite geometric series and sum of infinite geometric series by using formula of sum to infinite of geometric progression and use sigma notation to find the infinite sum of geometric sequences and series. Finally, there is a lecture on how to split infinite geometric series into two portions and solve for the sum to infinite of individual portions after which the two sums obtained are added together to get the required sum to infinite of the given special type of geometric series. This course offers a unique blend of mathematical exploration and real-world examples, making it both intellectually stimulating and visually engaging.

Who this course is for:
This course is for all level of students., Primary, secondary, college, tertiary, polythnic and university student will definitely find this lectures indispensable access for learning what sequences and series.