Question

the difference between the square of any two consecutive integers is equal to 1) sum of two numbers 2)difference of two numbers 3)an even numbers 4)product of two numbers

Answer 1

Given :  difference between the square of any two consecutive integers

To find : it is equal to

Solution:

Let say two consecutive integers are

N  & N + 1

difference between the square of  consecutive integers

= ( N + 1)² - N²

using a² - b² = (a+b)(a - b)

a = N + 1

b = N

= ( N + 1 + N)(N + 1 - N)

= 2N + 1

= N + (N + 1)

= Sum of two numbers

difference between the square of  consecutive integers  is equal to sum of two numbers

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