anonymous
  • anonymous
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.
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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anonymous
  • anonymous
|dw:1440269656166:dw|
anonymous
  • anonymous
1^3+2^3+3^#+...... \[1^3+2^3+3^3+...+n^3=\left( \sum_{}^{}n \right)^2\]
anonymous
  • anonymous
correction \[3^3\]

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anonymous
  • anonymous
correction 3^3 not 3^#
anonymous
  • anonymous
@surjithayer @mathmate @peachpi what does ^ mean
anonymous
  • anonymous
the symbol ^
anonymous
  • anonymous
exponent
anonymous
  • anonymous
ooohhhhhhhh. thx @peachpi
anonymous
  • anonymous
x^3 \[=x^3\]
anonymous
  • anonymous
\[\sum_{}^{}n=\frac{ n \left( n+1 \right) }{ 2 }\]
anonymous
  • anonymous
So how do I figure this out in "kids'" language
anonymous
  • anonymous
\[1+2+3+...+n=\frac{ n \left( n+1 \right) }{ 2 }\] put n=100 and simplify
anonymous
  • anonymous
What
anonymous
  • anonymous
\[\sum _{n=1}^{100} n^3=25502500 \]
anonymous
  • anonymous
\[1^3+2^3+3^3+...+100^3=\left( \frac{ 100\left( 100+1 \right) }{ 2 } \right)^2=\left( 50 \times 101 \right)^2=5050^2=?\]
anonymous
  • anonymous
In 7th grader words..... and what do all these slashes and { mean?
anonymous
  • anonymous
You know what \(\sum \) means?
anonymous
  • anonymous
nope.....
anonymous
  • anonymous
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
anonymous
  • anonymous
OHHH. I know what the word sum means I don't know why all of the () and / s are there
anonymous
  • anonymous
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 \[\sum_{n=1}^{100}n^3=\frac{ n^2(n+1)^2 }{ 4 }\]
anonymous
  • anonymous
so 100 = 1 What.... is there an answer???
anonymous
  • anonymous
change the n's to 100 100²(100+1)²/4
anonymous
  • anonymous
10000 x 10201 / 4
anonymous
  • anonymous
102,010,000 / 4
anonymous
  • anonymous
25502500
anonymous
  • anonymous
yes that's your answer
anonymous
  • anonymous
and how would I say cubic units
anonymous
  • anonymous
just put the words "cubic units" after the number
anonymous
  • anonymous
ok. Thank you so much!!!!!
anonymous
  • anonymous
you're welcome
anonymous
  • anonymous
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.
anonymous
  • anonymous
Here's a link to the formula. List it as a source http://www.9math.com/book/sum-cubes-first-n-natural-numbers
anonymous
  • anonymous
Thanks. Ill check it out

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