Question

hii frnds...


que no 14..

plz help...

no sparm...!!!

thank u..☺

Answer 1

Heya!!

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To show tht n^2 - n is divisible by 2 fr any positive integers ;

If n is an even no then it can be written in form of 2x where x is any + integer.

= (2x)^2 - 2x
= 4x^2 - 2x
= 2(2x^2 - x)
= 2m where m=2x^2 - x

Hence n^2 - n is divisible by 2 when n is an even no.

Try by odd no ;

If n is odd no then it can be written in form of 2x+1.

= (2x+1)^2 - (2x+1)
= 4x^2 +4x + 1 - 2x - 1
= 4x^2 +2x
= 2(2x^2 +1)
= 2m where m=2x^2 +1.

Hope it helps uh :)

Answer 2

Heya,

Let n be an even positive integer,

Let,
n = 2q
n² - n = (2q²) - 2q = 4q² - 2q = (2q - 1)
n - n = 2p , where p = q (2q - 1)
n² - n is divisible by 2

Let n be a odd positive integer,

Let,
n = 2q + 1
n²-n = = (2q + 1)² - (2q + 1)= (2q +1) ( 2q+1 -1)= 2q (2q + 1)
n² - n = 2p , where  p = q (2q + 1)
n² - n is divisible by 2.

Hope this will help you!!