Step 1: \ \

The statement is is divisible by . \ \

Condition I:

First show that, the above statement is true, when .

\ \

\ \

is divisible by . \ \

The statement is true for .

Condition I of the Principle of Mathematical Induction holds. \ \

Step 2:

Condition II :

Assume that   is divisible by .holds for some , and determine whether the formula then holds for . \ \

Assume that, is divisible by for some -----> equation (1). \ \

Now need show that, is divisible by . \ \

\ \

\ \

is divisible by and is divisible by . \ \

Therefore, is divisible by . \ \

Thus, Condition II also holds.

The statement is true for all natural numbers. \ \

Solution:

The statement is true for all natural numbers. \ \