Higher Algebra Hall & Knight Convergency & Divergency of Series (Chapter 21) Solutions
The Hall and Knight Higher Algebra Solutions for Chapter 21: Convergence and Divergence of Series are provided by subject matter experts at Instasolv to help you study for competitive exams like JEE Main and JEE Advanced. With the help of these solutions, you will understand that a series is an expression in which the successive terms are formed by some regular law. In case the series terminates at some assigned form, they are called finite series and if the number of terms is unlimited then it is called infinite series.
Higher Algebra Hall & Knight Chapter 21 ‘Convergence and Divergence of Series’ consists of 2 exercises with overall 33 questions. You can refer to these questions as practice material. By solving these questions, you will also study some crucial concepts like what is series, sequence, range and domain of series, finite and infinite series, convergent and divergent infinite series. All these topics are important for you if you are an engineering entrance exam aspirant.
Instasolv helps you by giving Hall & Knight Algebra Mathematics book with solutions. These are stepwise solutions for Convergence and Divergence of Series. These solutions are very accurate and are solved by our team of professionals so you can easily rely on them.
Important Topics for Hall and Knight Higher Algebra Solutions Chapter 21: Convergence and Divergence of Series
What is a Series or Sequence?
A series or sequence refers to a set of numbers that follows a rule to determine a successive term for example- x, x2, x3, x4… is a sequence of numbers. The domain of a series is a set of all-natural numbers. We use a term sigma in order to represent the summation of terms in a sequence.
Finite and Infinite Series
In simple words, the summation of a finite number of terms is called a finite series and the summation of an infinite number of terms and an upper limit of infinity is known as infinite terms. We have a sequence of infinite series that is ½, ¼, ⅛, 1/16. Now we will follow the rule and add them up i.e ½ + ¼ + ⅛ + 1/16…= S. We often solve the notation of infinite series using (sigma) that you will study in the chapter. An example of using sigma in infinite series using the above example is-
n=1½n = ½ + ¼ + ⅛ + 1/16 +…= 1
Convergent and Divergent Infinite Series
Convergent and divergent are the two types of series. When through some terms we achieve a final and constant term as n approaches infinity, it is said to be a convergent sequence. Series in which terms never become constant and continue to increase or decrease and approach to infinity is called divergent series.
If we suppose that n = x and the terms in a sequence is equal to fx. We now increase the value of x and take that to infinity if the f(x) value would become constant to a finite value, as x approaches infinity, then the sequence is convergent. On the other hand, if the f(x) values increase or decrease and reach infinity or -infinity, then it is called a divergent sequence.
Exercise Discussion of Hall & Knight Higher Algebra Solutions Chapter 21: Convergence and Divergence of Series
- There are overall 2 exercises in the Hall and Knight Higher Algebra Chapter 21 Convergence and Divergence of Series. Both the exercises comprise 33 questions.
- In the first exercise, there are 22 questions covering half the important concepts of the chapter. When you will solve this exercise you will learn how to find whether the given series is convergent or divergent, in situations where x and a being positive quantities or x and y being positive quantities, and you will test the series of the given terms.
- The second exercise comprises 12 questions which are limited to the rest of the concepts of the chapter. You will have to answer questions like finding whether the given series is convergent or divergent when a is a proper fraction.
- You can seek help from Instasolv if you get stuck at any question in the exercise. Our team has provided clear explanations in these solutions.
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