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Math Help - Simplify this equation w/ fractional expnents

  1. #1
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    Simplify this equation w/ fractional expnents

    I'm working on an induction problem, but can't show my work for simplifying this equation:

    1 - (1/2)^k + 1/2^(k+1) --------> Simplify ---------> 1 - (1/2)^(k + 1)

    I'm just assuming that's what it simplifys to. Can someone show me the work for this with the right answer if it's wrong.


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  2. #2
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    1-\left (\left (\frac{1}{2}  \right )^{k}-\left (\frac{1}{2}  \right )^{k+1}  \right )=1-\left ( \frac{1}{2} \right )^{k+1},you simplified right.
    Last edited by Raoh; November 26th 2009 at 08:07 AM.
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  3. #3
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    1-\left (\left (\frac{1}{2}  \right )^{k}-\left (\frac{1}{2}  \right )^{k+1}  \right ) =1- \left (\left (\frac{1}{2}  \right )^{k}-\left (\frac{1}{2}  \right )^k\left ( \frac{1}{2} \right )  \right ) =1-\left ( \frac{1}{2} \right )^k\left ( 1-\frac{1}{2} \right ) =1-\left ( \frac{1}{2} \right )\left ( \frac{1}{2} \right )^k =1-\left ( \frac{1}{2} \right )^{k+1}
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  4. #4
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    Hello everyone

    Alternatively you might find it easier to say
    1-\left(\frac12\right)^k+\left(\frac12\right)^{k+1}
    =1-2\times\left(\frac12\right)^{k+1}+1\times\left(\fr  ac12\right)^{k+1}

    =1-\left(\frac12\right)^{k+1}
    Grandad
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