Prove that the difference of the squares of 2 consecutive numbers is always the sum of the 2 numbers

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Mathematics

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12 January, 15:05

Prove that the difference of the squares of 2 consecutive numbers is always the sum of the 2 numbers

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Answers (1)

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Lola Duncan · Answer 1

see explanation

Step-by-step explanation:

let the 2 consecutive numbers be n and n + 1

sum = n + n + 1 = 2n + 1

and

(n + 1) ² - n² ← difference of the squares

= n² + 2n + 1 - n²

= 2n + 1 = sum of 2 numbers