Question

Prove that n2 + n is even , where n is natural number.?

Answer 1

simple,

n(n+1)

if n is odd then n+1 is even

hence product is even.

if n is even then also product is even.

Answer 2

n2 - n = (2q)2 - 2q = 4q2 - 2q = 2q (2q + 1 )

n2 - n = 2r , where r = q (2q - 1)

n2 - n is divisible by 2  

Case 2 When n = 2q + 1

In this case  

n2 -n = (2q + 1)2 - (2q + 1)= (2q +1) ( 2q+1-1)= 2q (2q + 1)

n2-n = 2r , where  r = q (2q + 1)

n2- n is divisible by 2.

As 2 is a even number

HENCE PROVED

PLS MARK BRAINLIEST