Prove the following by using the principle of mathematical induction for all n ∈ N: n (n + 1) (n + 5) is a multiple of 3

We can compose the given assertion as

 

   

, which is a different of

   

In the event that

   

we get

   

which is a various of

   

Which is valid.

Think about

   

be valid for some certain number

   

   

is a different of

   

   

where

   

Presently let us demonstrate that

   

is valid.

Here

   

We can compose it as

   

By duplicating the terms

   

So we get

   

Subbing condition

   

   

By increase

   

On additional computation

   

Accepting

   

as normal

   

We get

   

is some regular number

   

is a numerous of

   

   

is valid at whatever point

   

is valid.

Hence, by the rule of numerical enlistment, articulation

   

is valid for all regular numbers for example