Odisha State Board CHSE Odisha Class 11 Math Notes Chapter 5 Principles of Mathematical Induction will enable students to study smartly.

## CHSE Odisha 11th Class Math Notes Chapter 5 Principles of Mathematical Induction

**Principles Of Mathematical Induction**

(i) Principle – 1

Let P(n) is a statement , n ∈ Z

Step – 1: Verification step:

verify that P(1) is true.

Step – 2: Induction step – 1:

Assume that P(k) is true for any arbitrary k ∈ N.

Step – 3: Induction step – 2:

prove that P_{(k+1)} is true using step – 1 and step – 2

Step – 4: Conclusion Step:

If P_{(k+1)} is true then take a conclusion that by Principle of mathematical induction P(n) is true for all n ∈ N.

(ii) Principle – 2

Let P(n) be a statement, n ∈ N.

Step – 1: Verification step:

verify the P(1) is true

Step – 2: Induction step – 1:

Assume that P(2), P(3),….. P(k) is true.

Step – 3: Induction step – 2:

Using step – 1 and step – 2 prove that P(k + 1) is true.

Step – 4: Conclusion step:

If P(k + 1) is true, then take a conclusion that by Principle of mathematical induction P(n) is true for all n ∈ N.