Question

prove that n²-n is divisible by 2 for enemy positive integers​

Answer 1

Step-by-step explanation:

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rajeevgupta39

Primary SchoolMath 5+3 pts

Prove that n2+n is divisible by 2 for evry positive integer n.

Report by Kun3 25.05.2017

Answers

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Anustarnoor

Here is the answer to your question.

Any positive integer is of the form 2q or 2q + 1, where q is some integer

When n = 2q,

n²+n=(2q)²+2q

=4q²+2q

= 2q(2q+1)

which is divisible by 2

when n=2q+1

n²-n=(2q+1)²+(2q+1)

= 4q²+4q+1+2q+1

=4q²+6q +2

= 2(2q²+3q+1)

which is divisible by 2

hence n²+n is divisible by 2 for every positive integer n

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