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Updated in [August 31st, 2023]
Skills and Knowledge:
By taking this course, you will acquire the following Skills and Knowledge:
- Understanding of sigma notation and how to use it to write an average formula
- Knowledge of the sigma laws and how to use the mathematical induction technique
- Ability to identify and analyze different types of finite sequences
- Ability to list the first four terms of a sequence and its monotonic behaviour
- Understanding of enumerative, closed-form, and recursive definition
- Knowledge of the concept of convergence of series
- Ability to explain the Fibonacci sequence, the ratio of successive terms, and the golden ratio
- Understanding of how to count ordered partitions of n using 1's and 2's
- Knowledge of the theorem that can yield the sum of the first n terms of the Fibonacci sequence
- Ability to convert presented series into closed-form and vice-versa
- Understanding of how to subtract the second series from the first
- Knowledge of the process involved in taking the limit of both sides of the last equation
- Ability to explain the integral test, the determination of series when it converges or diverges, and the p-test for intervals and series
- Understanding of the ratio test, the alternating series test, and the alternating harmonic series
- Knowledge of the Maclaurin series and how the Taylor series can be a generalized form of the Maclaurin series centred at an arbitrary value.
Professional Growth:
This course contributes to professional growth by providing students with the necessary skills and knowledge to understand and apply mathematical concepts in a business setting. It covers topics such as sigma notation, the representation of sums of sequences, the mathematical induction technique, and the various types of finite sequences. It also covers topics such as the Fibonacci sequence, the ratio of successive terms, and the concept of the golden ratio. Additionally, the course covers topics such as the integral test, the determination of series when it converges or diverges, and the p-test for intervals and series. By taking this course, students will gain a better understanding of the fundamentals of sequences and convergence series, which will help them to be more successful in their business endeavors.
Further Education:
This course titled "Sequence and Convergence Series Maths for Business" is suitable for preparing for further education. It covers a wide range of topics related to sequences and convergence series, which are important concepts in mathematics. The course provides in-depth lessons on various techniques and formulas used in expressing large sums, as well as understanding the behavior and properties of different types of sequences. It also explores concepts such as mathematical induction, Fibonacci sequence, geometric series, and convergence tests. Overall, this course will enhance your mathematical skills and knowledge, making it beneficial for further education in business or any field that requires a strong foundation in mathematics.
Course Syllabus
Sequences and Series
This module will teach you about the formulas for sums of sequences, the sigma laws, factorial notation, as well as finite sequences. Learn about the arithmetic sequence, geometric sequence, binary sequence along with the power and triangular sequences.Tests for Convergence
This module will teach you the methods of determining whether or not an infinite series converges a comparison test. Discuss the divergent test for geometric series and how to find the coefficient. You will also learn about the interval and radius of convergence of a power series.Course assessment
