1 + 2 + 3 + … + n = n (n +1)/2 i.e., the sum of the first n natural numbers is n (n + 1)/2.

Let,

   

For,

   

   

   

So,

   

As, P (n) is true for

   

Let P (n) be the true for

   

, so

   

Now,

   

   

   

   

P (n) is true for

   

P (n) is true for all

   

So, by the principle of Mathematical Induction

Hence,

   

is true for all n ∈ N.