Mathematical Induction

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

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.
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.