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Find all f(k) such that \(\sum_{k=1}^n f(k) = n^3.\)

 Feb 10, 2020
 #1
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From the formulas 1 + 2 + .. + n = n(n + 1)/2 and 1^2 + 2^2 + ... + n^2 = n(n + 1)(2n + 1)/6, it follows that f(k) = k^4/4 + k^3/2 + k^2/4.

 Feb 10, 2020
 #2
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Thank you!

 Feb 10, 2020
 #3
avatar+29200 
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I get the following:

 

 Feb 10, 2020
 #4
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Find  \(f(k)\) such that \(\sum \limits_{k=1}^n f(k) = n^3\).

 

answer see: https://web2.0calc.com/questions/math-question-please-help_11

 

laugh

 Feb 10, 2020

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