Question

prove that n square + n is divisible by 2 for any positive integer

Answer 1

n=2q,2q+1. q for some integer
by putting the value on n square + n you can get the answer.
there will be two condition for first 2q
for second 2q+1

Answer 2

any even positive integer are in the form of 2q
or odd positive integer are in the form of 2q+1
formula are applicable for this -
$a = b \times q + r \\ where \: 0 \leqslant r < b$
for example 2q+1
here given a= 2q+1 (b=2)
according to question b>r
possibilities of r = 0,1
you can solve this in that way

if any doubt, please mention below