Higher Algebra Hall & Knight Recurring Series (Chapter 24) Solutions

The Hall & Knight Higher Algebra Solutions for Chapter 24 ‘Recurring Series’ are created by subject matter experts at Instasolv for IIT JEE and NEET preparation. This chapter discusses topics like recurrence relation, solving recurrence relations, and recurrence sequence. The exercise solutions will help you understand how to solve recurrence relations. You will also come across various recurrence series such as Fibonacci Series. 

Higher Algebra by Hall and Knight Solutions for Recurring Series consists of an exercise with a total number of 15 questions. You will learn to find the generating function and general term of a series, the sum and the nth term of a series, and will understand how to prove if a series is recurring. You can solve the exercise once you are done with the chapter for the purpose of practice. Once you study these questions in-depth you will be able to solve all the questions in JEE and NEET easily.

Instasolv will help you get the solutions for Elementary Algebra and Higher Algebra by Hall & Knight. Instasolv team gives you various tips and tricks to solve the questions efficiently. The solutions for Recurring Series are 100% accurate. We ensure that no mistakes are made and the main aim is to help you boost your confidence level by helping you to understand all the solutions to the questions.

Important Topics for Hall and Knight Higher Algebra Solutions Chapter 24: Recurring Series

What is a Recurrence Relation?

A recurrence relation is an equation that represents a rule-based sequence. It helps in finding the next term which is the subsequent term that depends upon the previous term or preceding term. In simple words, if in a given series a preceding term is given then we can easily find the subsequent term.

 It is very well known that according to a standard pattern that all the terms in relation have similar characteristics. For eg- if we are given a value of ‘n’ we can easily determine other values by using the value of ‘n’.

How to solve Recurrence Relations?

In order to solve recurrence relations, it is important to find the initial term first. Here is an example of a sequence:

 an = 2an-1-3an-2

  • Now, first of all, we need to check the initial conditions a0 = 1, a1= 2 that the sequence is of closed patter.
  • After this, try another initial condition and find a closed formula to it.
  • After trying different initial conditions the result produces a series.
  • Now, we will notice that the difference between each term also forms a sequence.
  • We are required to add all the terms of the new sequence in order to understand which sequence is formed.
  • If we understood the pattern it enables us to identify the initial condition of the recurrence relation. 

Examples of Recurrence Relations 

The examples of recurrence are based on series and sequence patterns. Following are a few examples we will discuss here:

  • Factorial representation 

Factorial is defined by using the recurrence relation concept such as:

 n! = n(n-1)!; n>0

When n = 0

0! = 1 is the initial condition

The factorial notation has to be expanded in order to find further values where the succeeding term is dependent upon the preceding term.

  • Fibonacci numbers

In series or Fibonacci numbers the last two preceding terms determine the succeeding terms. 

Fn = fn-1 + fn-2

Take the initial values now,

f0= 0, f1= 1

So, f2 = f1 + f0 = 0+1 = 1

What is a Recurrence Sequence?

A sequence is an ordered set of quantities. Therefore in recurring relations, a recurring sequence is a sequence that satisfies recurrence relation. In the chapter, you will study different types of recurring sequence.

Exercise Discussion of Hall & Knight Higher Algebra Solutions Chapter 24: Recurring Series

  • There is one exercise in the Higher Algebra By H.S. Hall and S.R. Knight book for Recurring Series. The exercise consists of overall 15 questions which are unsolved for practice purpose.
  • The exercise bears questions that cover the concepts discussed in the entire chapter. One you study the chapter to the core it will be easy for you to solve all the questions in the exercise. 
  • While solving the exercise you will face questions like finding the generating function and general term of the given series, show that the given series are recurring series and find their scales of relation or find the sum of 2n+x terms of the given series, and so on.
  • You will get access to all the solutions for the exercise of Recurring Series by Hall and Knight online at instasolv. 

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