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Thread: Calculate

  1. May 21st 2010, 07:39 PM #1
    dhiab
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    Calculate

    Calculate
    <br /> 2^{\frac{1}{4}}\times 2^{\frac{1}{8}}\times 2^{\frac{1}{16}}\times.... \times .....<br />
    Last edited by dhiab; May 21st 2010 at 08:04 PM.
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  2. May 21st 2010, 08:00 PM #2
    dwsmith
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    Quote Originally Posted by dhiab View Post
    Calculate
    <br /> 2^{\frac{1}{4}}\times 2^{\frac{1}{8}}\times 2^{\frac{1}{16}}\times \times .....<br />
    2^2\times 2^2=2^{2+2}

    \sum_{n=2}^{\infty}2^{x} where x=\frac{1}{2^n}
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  3. May 22nd 2010, 03:39 AM #3
    Soroban
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    Hello, dhiab!

    Calculate : . 2^{\frac{1}{4}}\times 2^{\frac{1}{8}}\times 2^{\frac{1}{16}}\times \hdots

    \text{We have: }\;2^{\overbrace{(\tfrac{1}{4}+\tfrac{1}{8}+ \tfrac{1}{16}+ \hdots)}^{\text{geometric series}}} \;=\;2^{\frac{1}{2}} \;=\;\sqrt{2}
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