To Prove:

Let us prove this question by principle of mathematical induction (PMI)

Let P(n):

For n = 1

LHS = = 12

RHS =

= = 12

Hence, LHS = RHS

P(n) is true for n = 1

Assume P(k) is true

……(1)

We will prove that P(k + 1) is true

…(2)

We have to prove P(k + 1) from P(k) ie (2) from (1)

From (1)

Adding both sides

which is the same as P(k + 1)

Therefore, P (k + 1) is true whenever P(k) is true.

By the principle of mathematical induction, P(n) is true for×

where n is a natural number

Put k = n - 1

Hence proved