# Higher Algebra Hall & Knight Mathematical Induction (Chapter 12) Solutions

Hall and Knight Higher Algebra Solutions for Chapter 12 ‘Mathematical Induction’ are created by subject matter experts at Instasolv to guide you for competitive exams like IIT JEE and NEET. These solutions comprise of all the essential topics which will help in forming a stronger command over the concepts of induction, mode of proof, terms in unity, theorems of divisibility and factors. Hall & Knight Algebra Mathematics book with solutions for Mathematical Induction also covers vital ideas regarding the factors of n-1, series, positive integrals and binomial factors. You will also learn about the concepts of conjecture, same form and index with the help of our solutions.

Higher Algebra by Hall & Knight ‘Mathematical Induction’ solutions includes 1 exercise with only 5 questions. Once you solve these questions you will learn how to prove the sum of different series by mathematical induction process. With only 5 questions, this chapter is pretty easier to solve and is also a part of the Class 12 board exams syllabus. So, you can practice a few important questions of the chapter with the help of our solutions.

Instasolv’s solutions for Higher Algebra By H.S. Hall and S.R. Knight Mathematical Induction** **have been prepared to make sure that your time is invested in enhancing your concepts and preparation rather than wasting time in your struggles for reaching out to various study resources. Our subject experts have ensured that you gain a complete understanding of the method of mathematical induction so that you can solve questions easily in your board exams as well as competitive tests.

## Important Topics for Hall and Knight Higher Algebra Solutions Chapter 12: Mathematical Induction

**Mathematical Induction **

As the name of the chapter suggests, you will begin by engaging with the concept of mathematical induction and understanding what it implies. You will learn that in mathematics we deal with a lot of formulas like those of profit, loss, interest, area and mean. But not all the formulas that we deal with in mathematics can be demonstrated by a direct mode of proof; in such scenarios where the demonstration tends to be impossible through direct means the method used is known as induction.

In this chapter, induction has been explained in detail along with solved examples and step by step guidance. This topic is very important for competitive exams as it helps in easy solutions of tricky and logic-based series.

**Method of Trial**

In Hall and Knight Higher Algebra Mathematical Induction solutions, while you will learn to implement the idea of induction, you will also learn about the initial steps through which the equations are examined. Most of the questions that you will encounter are based such that they are present in the form of equations or conditions where they have been assigned a value and you are required to prove whether they stand true to the given values with respect to the conditions given in the question. The first step of solving questions with respect to induction is the method of trial. This is basically a step of verification where you check whether or not the given statement given in the question is true.

### Exercise Discussions of Hall and Knight Higher Algebra Solutions Chapter 12: Mathematical Induction

**Example XII**

**This chapter has a very concise section for exercise questions****There are just 5 questions in the unsolved examples**- The first question of the exercise requires you to prove that the given series is equal to the square of n
- The second question presents two equations, one that is a series and the other which is a proper expression, you have required to prove that both the equations stand equal to each other
- The same kind of an approach is seen in the third question where again you are required to equate the two expressions by making use of the fundamentals of induction and prove that they stand equal to each other.
- The last question is based on a word format where you are provided with an expression that has its power raised to the variable n and you need to prove that the expression is divisible by (x + y) keeping in mind the condition that n is an even value.

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