Question

Use the Principle of Mathematical Induction to show that the given statement is true for all natural numbers n.

Answer 1

Step 1:

The statement is .

Condition I:

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

Left hand side

Right hand side

The statement is true for .

Condition 1 of the Principle of Mathematical Induction holds.

Step 2:

Condition II :

Assume that holds for some ,

 

and determine whether the formula then holds for .

Assume that, for some . -----> equation (1).

Now need show that,

Left hand side

From equation (1).

= Right hand side

Thus, Condition II also holds.

The statement is true for all natural numbers.

Solution:

The statement is true for all natural numbers.