# Mathematical Induction

Subject: Mathematics Exam: AP EAMCET Engineering

Chapter Rating: Do If You Have Time

Topic Weightage:

Chapter Rating: Do If You Have Time

Topic Weightage:

**0.02**## Start a discussion on this chapter

## Doubts and Discussions on this chapter

manisha started a discussion - can u plz provide chapter wise... - Participate

Sindhuja D... started a discussion - how to solve the eamcet bits - Participate

Sindhuja D... started a discussion - how to solve the eamcet bits - Participate

## Important Concepts in Mathematical Induction

Find notes, videos, important points and questions to practice on each of these concepts.

- Principles of Mathematical Induction
- Application of Induction

## My Chapter Prep Status

## Chapter Expert Trophy

pinkee

How can you win?

You need to score more than 414 marks to beat pinkee

parimala, lasya, Alekhya PVSNS

How can you win?

You need to score more than 414 marks to beat pinkee

**Others In The Race!**parimala, lasya, Alekhya PVSNS

## Important Points

**FIRST PRINCIPLE OF MATHEMATICAL INDUCTION**

Step I: Actual verification of the proposition for the starting value '

*i*'.

Step II: Assuming the proposition to be true for '

*k*',

*k*>=

*i*and then providing that it is true for the value (

*k*+1) which is the next higher integer.

Step III: Combine the two steps or let

*P*(

*n*) be a statement involving natural number

*n*. To prove statement

*P*(

*n*) is true for all natural number we use following process:

1. Prove that

*P*(1) is true.

2. Assume

*P*(

*k*) is true

3. Using (1) and (2) prove that statement is true for

*n*=

*k*+1,

*i.e*.,

*P*(

*k*+1) is true.

This is first principle of Mathematical Induction.

**SECOND PRINCIPLE OF MATHEMATICAL INDUCTION**

Step I: Actual verification of the proposition for the starting value

*i*and (

*i*+1).

Step II: Assuming the proposition to be true for

*k*-1 and then proving that it is true for the value (

*k*+1):

*k*>=

*i*+1.

Step III: Combine the above two steps these are used to solve problem or in 2nd principle of Mathematical Induction following steps are used:

1. Prove that P(1) is true

2. Assume

*P*(

*n*) is true for all natural number such that 2<=

*n*<

*k*

3. Using (1) and (2) prove that

*P*(

*k*+1) is true.