“The product of two consecutive positive integers is divisible by 2”. Is this statement true or false? Give reasons

Solution:

True,

n, (n + 1) can be the two consecutive integers. One will be odd and the other one will be even. So, one integer out of these two must be divisible by 2

Therefore, the product of two consecutive integers is divisible by 2.

✦ Try This: Prove that the product of two consecutive positive integers is divisible by 2

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 an 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 + 6k + 2

= 2(2k² + 3k + 1)

Clearly the product is divisible by 2.

Therefore, the product of two consecutive integers is divisible by 2

The product of two consecutive positive integers is divisible by 2”. Is this statement true or false? Give reasons

☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 1

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NCERT Exemplar Class 10 Maths Exercise 1.2 Problem 2

“The product of two consecutive positive integers is divisible by 2”. Is this statement true or false? Give reasons

Summary:

True, The product of two consecutive positive integers is divisible by 2

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