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Math Help - Quickie #1

  1. #1
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    Quickie #1

    Evaulate: . \left(\frac{1\!\cdot\!2\!\cdot\!4 \,+ \,2\!\cdot\!4\!\cdot\!8 \,+ \,3\!\cdot\!6\!\cdot\!12 \,+ \,\cdots}{1\!\cdot\!3\!\cdot\!9 \,+ \,2\!\cdot\!6\!\cdot\!18 \,+ \,3\!\cdot\!9\!\cdot\!27 \,+ \,\cdots}\right)^{\frac{1}{3}}

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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by Soroban View Post
    Evaulate: . \left(\frac{1\!\cdot\!2\!\cdot\!4 \,+ \,2\!\cdot\!4\!\cdot\!8 \,+ \,3\!\cdot\!6\!\cdot\!12 \,+ \,\cdots}{1\!\cdot\!3\!\cdot\!9 \,+ \,2\!\cdot\!6\!\cdot\!18 \,+ \,3\!\cdot\!9\!\cdot\!27 \,+ \,\cdots}\right)^{\frac{1}{3}}

    . \left(\frac{1\!\cdot\!2\!\cdot\!4 \,+ \,2\!\cdot\!4\!\cdot\!8 \,+ \,3\!\cdot\!6\!\cdot\!12 \,+ \,\cdots}{1\!\cdot\!3\!\cdot\!9 \,+ \,2\!\cdot\!6\!\cdot\!18 \,+ \,3\!\cdot\!9\!\cdot\!27 \,+ \,\cdots}\right)^{\frac{1}{3}}

    ............. =\frac{(1\cdot 2\cdot 4)^{1/3}}{(1\cdot 3\cdot 9)^{1/3}}\frac{(1+2+3+...)^{1/3}}{(1+2+3+...)^{1/3}}=\frac{2}{3}

    RonL
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  3. #3
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    Well done, Captain!
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