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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 March 4, 2021, 6:05 pm ad1c9bdddf
    https://brainmass.com/math/basic-algebra/induction-mathematical-proof-odd-even-powers-28445

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    Solution Preview

    Because,
    (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.

    $2.49

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