Anonymous
Anonymous asked in Science & MathematicsMathematics · 1 month ago

Math problem?

Evaluate: [(1*2*4+2*4*8+3*6*12+.....)/(1*3*9+2*6*18+3*9*27+....)]^(1/3)

I found this in a facebook group and the answer is 2/3. But if I input this in wolfram, the answer 1.

3 Answers

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  • 1 month ago

    [(1*2*4 + 2*4*8 + 3*6*12 +.....) / (1*3*9 + 2*6*18 + 3*9*27+....)]^(1/3)

    = [(8 + 64 + 216 +.....) / (27 + 216 + 729 +....)]^(1/3)

    = [(2^3 + 4^3 + 6^3 + ....) / (3^3 + 6^3 + 9^3 + ...)]^(1/3)

    = (2 + 4 + 6 + ....) / (3 + 6 + 9 + ...)

    = 2/3 + 2/3 + ......

    = 2/3

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  • Alan
    Lv 7
    1 month ago

    Wolfram Alpha did not correctly understand the ellipses.  

    if you enter 

    [(1*2*4+2*4*8+3*6*12)/(1*3*9+2*6*18+3*9*27)]^(1/3)  it says  = 2/3 

    if you enter 

    [(1*2*4+2*4*8+3*6*12+4*8*16 + 5*10*20 )

    /(1*3*9+2*6*18+3*9*27+ 4*12*36 +5*15*45 )]^(1/3) 

    = 2/3 

    but when you add the ellipse 

    it doesn't really understand what you mean 

    If you can write it as summation , I expect Wolftram Alpha 

    will get the right answer (I was wrong, it couldn't handle the 

    summation , said undefined) . 

    But does not seem to follow the ellipses. 

    Attachment image
    • Alan
      Lv 7
      1 month agoReport

      So what do the ellipse imply  "..." goes on forever or  ... goes on to the nth value 

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  • x * 2x * 4x => 8x^3

    x * 3x * 9x => 27x^3

    So what you have is:

    (8 * 1^3 + 8 * 2^3 + 8 * 3^3 + 8 * 4^3 + .... + 8 * n^3) / (27 * 1^3 + 27 * 2^3 + 27 * 3^3 + .... + 27 * n^3) =>

    (8/27) * (1^3 + 2^3 + 3^3 + 4^3 + ... + n^3) / (1^3 + 2^3 + ... + n^3) =>

    (8/27) * 1 =>

    (8/27)

    (8/27)^(1/3) =>

    2/3

    Without knowing how exactly how you did the input in wolfram, it's impossible for me to demonstrate where you went wrong.

    • Alan
      Lv 7
      1 month agoReport

      It gets it wrong with the  

      "..."  ellipses are being used.     
      I am not sure you should expect it to understand exactly what they meant by  
      "..." anyway

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