What is the sum of cubes in a series up to 'n' terms?

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The discussion focuses on finding the sum of a series of cubes up to 'n' terms, specifically the expression (1^3 / 1) + (1^3 + 2^3 / 1+2) + (1^3 + 2^3 + 3^3 / 1+2+3) and so on. The relevant formulas for the sum of cubes and the sum of integers are provided, but the initial attempt at a solution mistakenly yields the sum of squares instead. Evaluating the first few terms reveals a pattern of triangular numbers: 1, 3, 6, 10, and 15. The discussion emphasizes the need to correctly compute the sum of cubes for accurate results.
draotic
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Homework Statement


find the sum of the series to 'n' terms
(1^3 / 1 ) + (1^3 + 2^3 / 1+2 ) + (1^3 + 2^3 + 3^3 / 1+2+3 ) +...


Homework Equations



sigma n^2 = n(n+1)(2n+1) / 6
sigma n = n(n+1) / 2


The Attempt at a Solution


numerator = 1^3 + 2^3 + ... n^3
denominator = 1+2+3+...n
...
my answer comes out to be n(n+1) / 2 , but i think that's wrong...
please lead me
 
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That is the last term you are calculating. And anyway, the question says Sum of cubes (not squares) in numerator. If you evaluate first few terms, you get 1+3+6+10+15+...
I think you can work this out.
 

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