(a)

The statement is .

.

.

Rewrite the statement is .

Condition I:

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

.

The statement is true for .

Condition I of the Principle of Mathematical Induction holds.

Condition II :

Assume that , holds for some , and determine whether the formula then holds for .

Substitute .

.

Check the condition for .

Substitute .

.

The formula is true for all natural numbers .

(b)

The statement is .

.

Rewrite the statement is .

Condition I:

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

The statement is true for .

Condition I of the Principle of Mathematical Induction holds.

Condition II :

Assume that , holds for some , and determine whether the formula then holds for .

Substitute .

.

Check the condition for .

Substitute .

(a) The formula is true for all natural numbers .

(b) The formula is true for all natural numbers .