Prove each of the statements in 4n – 1 is divisible by 3, for each natural number n.

 

As per the inquiry,

   

is separable by 3.

Thus, subbing various qualities for n, we get,

   

which is distinguishable by 3.

   

which is detachable by 3.

   

which is distinct by 3.

   

which is distinct by 3.

Let

   

be detachable by 3,

In this way, we get,

   

.

Presently, we likewise get that,

   

   

   

is detachable by 3.

   

is valid when P(k) is valid

Hence, by Mathematical Induction,

   

is detachable by 3 is valid for every regular number n.