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14 May, 17:52

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

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  1. 14 May, 21:44
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    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
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