In this set of Math Tutorials we cover Sequences and Series in detail with clear guides, Sequences and Series formulas and working examples. Each tutorial includes example questions, a revision guide and supporting Sequences and Series calculators.
We also provide online Sequences and Series Calculators which allow you to calculate specific Sequences and Series formula in support of the tutorials or to check and verify your own calculations in support of your Sequences and Series homework, math coursework or to help you improve your own understanding so it is easier to teach your children Sequences and Series.
|12.1||Working with Term-to-Term Rules in Sequences|
|12.2||Working with Arithmetic and Geometric Series. How to find the Sum of the First n-Terms of a Series.|
|12.3||Binomial Expansion and Coefficients|
|12.4||Infinite Series Explained|
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This chapter deals with number sequences and series. The first tutorial focuses on general points regarding sequences such as the meaning and definition of sequences in math; their components and types, etc. Then, the tutorial continues with sequence notation and methods used to find the nth term of sequences - including combined ones - in a variety of situations and methods, where the focus will mainly be on linear and quadratic sequences.
The second tutorial of this chapter is dedicated to the number series. It begins with the definition of number series and their difference with number sequences. Then, it follows with the Gauss method used for finding the sum of n-terms in arithmetic series and showing how to calculate the sum of the first n-terms in an arithmetic series without using the Gauss formula. The second tutorial continues with increasing and decreasing geometric series (definition, the difference with arithmetic series, formula, etc.). The last part of this tutorial deals with things like how to combine number sequences and series to find any missing information; how to deal with combined series; how to apply the number sequences and series in practice; etc.
The third tutorial deals with binomial expansion and coefficients, as a more advanced approach to binomials (polynomials with two terms) discussed in the previous chapter covering Polynomials. Questions like, "what are the coefficients of binomial expressions"; "how to expand binomial expressions with small powers"; "why it is not suitable to use the FOIL Rule in higher power binomial expansions", etc., are discussed in the first part of this tutorial. Then, the tutorial continues with Pascal's Triangle and its use in determining the coefficients of binomial expressions including the advantages and limitations that Pascal's Triangle has for binomial coefficients. A theorem, known as the Binomial Coefficient Theorem, and the advantages it provides in finding the coefficients of a binomial expression are explained, as well as the methods of expanding other types of binomials that are not expressed in the standard form.
The fourth and last tutorial of this chapter deals with infinite series. The definition of infinite series and the distinction between finite and infinite series are explained. Then the tutorial continues with diverging and converging infinite series and how to find the sum of all terms in converging geometric infinite series. Towards the end of the tutorial questions like, "what are some special types of infinite series"; "what is the ratio convergence test and the root convergence test" and why do we use them, are answered.
The following Math Calculators are provided in support of the Sequences and Series tutorials.