**Mathematical Induction is the science of proving a statement, that means true or false for all natural positive integers.**There are basically three principles involved for proving mathematical induction. Here we will see how to solve mathematical induction;

The principle of Mathematical Induction is given below:

To prove result is true for p = 1,

Assume that result is true for p = m,

To prove result is true for p = m + 1,

Third principle is an important Principle of Mathematical Induction.

Let’s take an example of mathematical induction:

Suppose we have to use mathematical induction for given series 1 + 2 + 3 +………..+ p = p (p + 1)/2 for all positive integers ‘p’.

Step 1: To prove result is true for p = 1,

L.H.S = p,

= (1),

= 1.

Now, R.H.S = p (p + 1)/2,

= 1(1+1)/2,

= 2/2,

= 1.

Hence, L.H.S = R.H.S so result is true for p = 1.

Step 2: Assume that result is true for p = m.

= 1 + 2 + 3 +………..+ m = m (m + 1)/2,

Step 3: To prove result is true for p = m + 1,

In this step we have to replace ‘p’ with (m + 1) to both the sides of the series. So,

We have to show 1 + 2 + 3 +………..+ (m + 1) = m + 1[(m + 1) + 1]/2

L.H.S

= 1 + 2 + 3 +………..m + (m + 1).

From step 2

= m (m + 1)/2 + (m + 1),

= [m (m + 1) +2 (m + 1)] / 2,

= (m + 1)[m + 2]/2,

= (m + 1) [(m + 1) + 1] / 2,

Hence L.HS = R.H.S so result is true for p = m + 1.