Question

7. Prove that n^2-n is divisible by 2 for every positive
integer n.​

Answer 1

Step-by-step explanation:

every positive integer can be of the form 2q, 2q+1

when n=2q

n^2-n= 4q^2-2n

=2m (where m = 2q^2-1)

therefore it is divisible by 2

when n=2q+1

n^2-n=4q^2+1-4q-2q+1

=2m (where m= 2q^2+1-2q^2)

therefore it is divisible by two

hence proved

Answer 2

Answer:

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