Sequence and Convergence Series Maths for Business
Free online course on the sequence of partial sums, convergence of series and sequences defined by a recursive formula.Publisher: ADU
CertificationView course modules
Sequence and Convergence Series Maths for Business is a free online course that aims to provide you with in-depth illustrations on convenient ways of expressing large sums. It is important to understand how to represent an odd number, dummy variable and how to use sigma notation to write an average formula. Before working with the formulas for the sums of sequences, it is important to understand the sigma laws. This course will take you through how to use the mathematical induction technique, as well as the representation of the sigma sum. This course introduces you to the various types of finite sequences, sequences defined by a recursive formula, arithmetic sequence and geometric sequence. Have you considered analyzing how triangular numbers can be written as the sum of consecutive positive integers? This course will teach you the essential techniques that can be adopted.
If you want to explore how a sequence can be bounded to converge, how to list the first four terms of sequence and the monotonic behaviour of a sequence, then sign up for this course. Having completed this course, you will be able to explain enumerative, closed-form, recursive definition, as well as the concept of convergence of series. Next, this course will help you understand the Fibonacci sequence, the ratio of successive terms, as well as the concept of the golden ratio. Do you know the counting trick of counting ordered partitions of n using 1's and 2's? The course also analyzes the theorem that can yield the sum of the first n terms of the Fibonacci sequence. Sequence and Convergence Series Maths for Business course explains how to convert presented series into closed-form and vice-versa. This course seeks to clarify any challenges you may face in understanding geometric series and how divergence theorem can be used to indicate the necessary condition.
Furthermore, you will also learn about the process involved in subtracting the second series from the first, as well as how to take the limit of both sides of the last equation. You will also learn about the concept of the integral test, the determination of series when it converges or diverges, as well as the p-test for intervals and series. Do you know there is a specific analysis for the ratio test? This course will help you get a better understanding of the alternating series test and alternating harmonic series. This course will explain in detail the Maclaurin series and how the Taylor series can be a generalized form of the Maclaurin series centred at an arbitrary value. This free online will be of great interest to students, researchers, and anyone with an interest in the fundamentals of sequences and convergence series. Register for this course and improve your skills in mathematics for business like a pro!Start Course Now
Sequences and Series
Sequences and Series - Learning Outcomes
Sigma Notation and Variable Number of Terms
Formula for Sums of Sequences
The Fibonacci Sequence
Sequences and Series - Lesson Summary
Tests for Convergence
Tests for Convergence - Learning Outcomes
Divergence and Comparison Tests
The Integral Test
Ratio Test and Alternating Series Test
Maclaurin and Taylor Series
Finding the Coefficients
Great Shortcuts for Finding Series
Tests for Convergence - Lesson Summary
Upon completion of this course, you should be able to:
- Identify the formulas for sums of sequences and the sigma laws.
- Explain the concept of factorial notation, as well as finite sequences.
- Examine the arithmetic sequence, geometric sequence and binary sequence.
- Analyze the methods for determining divergent test for geometric series.
Identify the great shortcuts for finding series, as well as how to find the coefficients.
- Explain the concept of the interval and radius of convergence of a power series.
- Discuss whether an infinite series can converge an alternating series test.
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