Question

prove that n²-n is divisible by two for every positive integer n.

Answer 1

n² - n

= n ( n - 1 )

= ( n - 1 ) n.

So , n²-n is the product of two consecutive numbers.

We know that, In two consecutive numbers, one of them would be divisible by 2 .

Hence, the product would be divisible by 2 .

So, n²-n is divisible by 2 for every positive integer " n "

Answer 2

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