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Prove that the product of two consecutive positive integer is divisible by2

Posted by Saloni Tiwari 6 years, 2 months ago

CBSE > Class 10 > Mathematics

1 answers

Yogita Ingle 6 years, 2 months ago

Let the two consecutive positive integers be x and x + 1

Product of two consecutive positive integers = x (x + 1)= x² + x

Case (i): x is even number

Let x = 2k
⇒x² + x = (2k)²+ 2k
= 4k² + 2k
= 2k ( 2k + 1)

Hence the product is divisible by 2

Case (ii): x is odd number

Let x = 2k + 1
⇒ x² + x = (2k + 1)² + (2k + 1)
= 4k² + 4k + 1 + 2k + 1
= 4k² + 6k + 2
= 2 (2k² + 3k + 1)

Clearly the product is divisible by 2

From the both the cases we can conclude that the product of two consecutive positive integers is divisible by 2.

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