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Math Help - simple show that

  1. #1
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    simple show that

    I'm trying to prove that:

    (1+x)^-5/2 < 1

    Sorry I know it's really easy but I'm just not seeing what to do!

    Thanks in advance!
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  2. #2
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    The very easiest thing to do, and always do this first, is give a good try at disproving it, rather than assuming it can be shown.

    Try x = -0.90 and see what you get for the left-hand side.
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  3. #3
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    Hello, hunkydory19!

    As given, the statement is not true . . .


    Prove: . (1+x)^{-5/2} \:<\:1
    It is necessary that  x > 0.


    Then we have: . 1 + x \:>\:1

    Raise both sides to the power \frac{5}{2}\!:\;\;(1 + x)^{\frac{5}{2}} \:>\:1

    Take reciprocals: . \frac{1}{(1+x)^{\frac{5}{2}}} \:<\:1\quad\Rightarrow\quad(1+x)^{-\frac{5}{2}} \:<\:1

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  4. #4
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    Thank you so much Soboran that was loads of help!

    Can I just ask what would happen if it was:

    (1+x)^-5/2 > 0

    because I wouldn't be able to do the reciprocal stage....

    thanks again!
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  5. #5
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    Can I just ask what would happen if it was:

    (1+x)^-5/2 > 0
    <br />
(1+x)^{-5/2}= ((1+x)^{-5})^{1/2}

    which is greater than or equal to 0 by definition of ^{1/2}
    Last edited by badgerigar; January 10th 2008 at 05:42 PM. Reason: fixed latex
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