Prove the following by using the principle of mathematical induction for all n ∈ N: 32n + 2 – 8n – 9 is divisible by 8

We can compose the given assertion as

is separable by

   

In the event that

   

we get

, which is distinguishable by

   

Which is valid.

Think about

   

be valid for some sure number

   

is distinct by

   

Presently let us demonstrate that

   

is valid.

Here

We can compose it as

By adding and taking away

   

we get

On additional improvement

 

From condition

   

we get

   

By duplicating the terms

   

So we get

   

By taking out the normal terms

   

   

, where

   

is a characteristic number

So is distinct by

   

   

is valid at whatever point

   

is valid.

 

Hence, by the rule of numerical acceptance, articulation

   

is valid for all regular numbers for example