prove that n^2 - n is divisible by 2
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8
n^2-n
( taking n as common )
n ( n - 1 )
Let, n be even
Then n(n-1) is divisible by 2.
Let, n be odd
Then (n-1) will be even, and n(n-1) is divisible by 2.
( taking n as common )
n ( n - 1 )
Let, n be even
Then n(n-1) is divisible by 2.
Let, n be odd
Then (n-1) will be even, and n(n-1) is divisible by 2.
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Answered by
3
=n^2-n
=n(n-1) (taking n common).
When n is odd the outer n will be odd and the value inside the brackets will be even as it is n-1,and we know that the multiplication of any odd number and even number will be even. And any even number is divisible by 2.
= n(n-1)
When n is even the outer n will be even and the value inside the brackets will be odd as it is n-1,and we know that the multiplication of any odd number and even number will be even. And any even number is divisible by 2.
Thus proving n^2- n is divisible by 2.
Hope it helps.
=n(n-1) (taking n common).
When n is odd the outer n will be odd and the value inside the brackets will be even as it is n-1,and we know that the multiplication of any odd number and even number will be even. And any even number is divisible by 2.
= n(n-1)
When n is even the outer n will be even and the value inside the brackets will be odd as it is n-1,and we know that the multiplication of any odd number and even number will be even. And any even number is divisible by 2.
Thus proving n^2- n is divisible by 2.
Hope it helps.
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