Question

Why does
n^2 = (n-1)^2 + (n-1) + n

Answer 1

left hand side of the equation is
= (n-1)^2+(n-1)+n
=n^2-2n+1+n-1+n
=n^2-2n+2n+1-1
=n^2
the right hand side

Answer 2

thanks