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anonymous

  • one year ago

The cubes in the diagram have sides of 1, 2, and 3, respectively. If the pattern continues, what will be the sum of the volumes of the first 100 cubes in the sequence? Express your answer in cubic units.

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  1. anonymous
    • one year ago
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    |dw:1440269656166:dw|

  2. anonymous
    • one year ago
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    1^3+2^3+3^#+...... \[1^3+2^3+3^3+...+n^3=\left( \sum_{}^{}n \right)^2\]

  3. anonymous
    • one year ago
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    correction \[3^3\]

  4. anonymous
    • one year ago
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    correction 3^3 not 3^#

  5. anonymous
    • one year ago
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    @surjithayer @mathmate @peachpi what does ^ mean

  6. anonymous
    • one year ago
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    the symbol ^

  7. anonymous
    • one year ago
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    exponent

  8. anonymous
    • one year ago
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    ooohhhhhhhh. thx @peachpi

  9. anonymous
    • one year ago
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    x^3 \[=x^3\]

  10. anonymous
    • one year ago
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    \[\sum_{}^{}n=\frac{ n \left( n+1 \right) }{ 2 }\]

  11. anonymous
    • one year ago
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    So how do I figure this out in "kids'" language

  12. anonymous
    • one year ago
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    \[1+2+3+...+n=\frac{ n \left( n+1 \right) }{ 2 }\] put n=100 and simplify

  13. anonymous
    • one year ago
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    What

  14. anonymous
    • one year ago
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    \[\sum _{n=1}^{100} n^3=25502500 \]

  15. anonymous
    • one year ago
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    \[1^3+2^3+3^3+...+100^3=\left( \frac{ 100\left( 100+1 \right) }{ 2 } \right)^2=\left( 50 \times 101 \right)^2=5050^2=?\]

  16. anonymous
    • one year ago
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    In 7th grader words..... and what do all these slashes and { mean?

  17. anonymous
    • one year ago
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    You know what \(\sum \) means?

  18. anonymous
    • one year ago
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    nope.....

  19. anonymous
    • one year ago
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    It means sum. It's shorthand so instead of adding up 1³, 2³, 3³, all the way to 100 @surjithayer gave you a short hand formula

  20. anonymous
    • one year ago
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    OHHH. I know what the word sum means I don't know why all of the () and / s are there

  21. anonymous
    • one year ago
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    n is the amount of numbers you want to add up. That's 100. So plug 100 into this the right side of this formula \[\sum_{n=1}^{100}n^3=\frac{ n^2(n+1)^2 }{ 4 }\]

  22. anonymous
    • one year ago
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    so 100 = 1 What.... is there an answer???

  23. anonymous
    • one year ago
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    change the n's to 100 100²(100+1)²/4

  24. anonymous
    • one year ago
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    10000 x 10201 / 4

  25. anonymous
    • one year ago
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    102,010,000 / 4

  26. anonymous
    • one year ago
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    25502500

  27. anonymous
    • one year ago
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    yes that's your answer

  28. anonymous
    • one year ago
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    and how would I say cubic units

  29. anonymous
    • one year ago
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    just put the words "cubic units" after the number

  30. anonymous
    • one year ago
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    ok. Thank you so much!!!!!

  31. anonymous
    • one year ago
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    you're welcome

  32. anonymous
    • one year ago
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    If I Have to show my work I would just out down the formula but Im a 7th grader so I want my teacher to believe me too.

  33. anonymous
    • one year ago
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    Here's a link to the formula. List it as a source http://www.9math.com/book/sum-cubes-first-n-natural-numbers

  34. anonymous
    • one year ago
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    Thanks. Ill check it out

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