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    Induction Mathematical Proof and Odd and Even Powers

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    Show that any positive integral power of (√2 - 1) can be written in the form √N -
    √(N-1) , where N is a positive integer.
    Hint: Use mathematical induction and consider separately the odd and even powers of (√2 - 1).

    We need to prove the following statement.

    Statement : For any positive n, (√2 - 1)ⁿ = √N - √(N-1) for some positive integer N.
    Note: N depends on n.

    Before we prove the above statement, we will prove a theorem below.

    Please see attachment for full question.

    © BrainMass Inc. brainmass.com November 24, 2022, 11:54 am ad1c9bdddf


    Solution Preview

    (sqrt(2) - 1)^n = sqrt(2a^2) - ...

    Solution Summary

    This is a proof regarding integral powers. The induction mathematical proof and odd and even powers.