** Statement: A sentence which is either exactly true or exactly false is called a statement**.

Example: “26 is divisible by 5” is a statement.

“25 is divisible by 2 and 5” is a statement.

**By Principle of Mathematical Induction, we can prove a mathematical statement true or false. **

If a statement satisfies the following three steps, the statement will be correct.

** Step 1: **To prove a statement P(n) is true for first natural number1. [P(1) is true].

** Step 2:** To consider the statement P(n) is true for any other natural number. [Let P(m) is true].

** Step 3:** To prove the statement P(n) is true for a natural number (m + 1). [To prove P(m + 1) is true]

__Example 1:__

Prove that .

__Solution: __

__Step 1:__

** Step 2: **Let P(m) is true.

** Step 3: **To prove P(m+1) is true.

** Example 2: **Prove that: is divisible by 576.

__Solution:__

__Step 1:__

576 is divisible by 576.

** Step 2: **Let P(m) is true.

**Step 3: **To prove: P(m+1) is true.

is divisible by 576.

Hence P(n) is true for

__Example 3:__

__Solution: __

__Step 1:__** **

is true.

** Step 2:** Let P(m) is true.

** Step 3: **To prove P(m+1) is true.

From equation (1)

Multiplying both sides by

is true.

Here, P(n) is true for .