Question

show that n²-n is divisible by 2

Answer 1

Hey mate!

here's your answer:

Firstly, let n = 2q  

n²-n = (2q)²-2q  

= 2q(2q-1)  

2m,when m=q(2q-1)  

Which is divisible by 2  

n = 2q+1  

n²-n = (2q+1)(2q+1-1)  

= 2q(2q+1)  

2m, when m=q(2q+1)  

Which is divisible by 2 hence ,n²-n is divisible by 2 for every positive integer n.

i hope it will be helpful to you