# Mathematical Induction

## Start a discussion on this chapter

## Doubts and Discussions on this chapter

praful jog... started a discussion - 2*7^n +3*5^n -5 is divisible b... - Participate

praful jog... started a discussion - 2*7^n +3*5^n -5 is divisible b... - Participate

Shivam started a discussion - 2^2n +1 has 7 in units place f... - Participate

ashok.taur... started a discussion - 2^2n +1 has 7 in units place f... - Participate

praful jog... started a discussion - 2*7^n +3*5^n -5 is divisible b... - Participate

Shivam started a discussion - 2^2n +1 has 7 in units place f... - Participate

ashok.taur... started a discussion - 2^2n +1 has 7 in units place f... - Participate

## Important Concepts in Mathematical Induction

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

Not So Important Concepts (Do if you have time)

Not So Important Concepts (Do if you have time)

- Principles of Mathematical Induction
- Application of Induction

## My Chapter Prep Status

## Chapter Expert Trophy

yashwanth2

How can you win?

You need to score more than 642 marks to beat yashwanth2

chanchal, yendunaidu2001, Sreeja

How can you win?

You need to score more than 642 marks to beat yashwanth2

**Others In The Race!**chanchal, yendunaidu2001, Sreeja

## 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.