Lesson plan
Squared triangular number
In number theory, the sum of the first cubes is the square of the th triangular number. That is, : 1^3+2^3+3^3+\cdots+n^3 = \left(1+2+3+\cdots+n\right)^2. The same equation may be written more compactly using the mathematical notation for summation: : \sum_{k=1}^n k^3 = \left(\sum_{k=1}^n k\right)^2. This identity is sometimes called Nicomachus's theorem, after Nicomachus of Gerasa ( ).
Article summary
In number theory, the sum of the first cubes is the square of the th triangular number. That is, : 1^3+2^3+3^3+\cdots+n^3 = \left(1+2+3+\cdots+n\right)^2. The same equation may be written more compactly using the mathematical notation for summation: : \sum_{k=1}^n k^3 = \left(\sum_{k=1}^n k\right)^2. This identity is sometimes called Nicomachus's theorem, after Nicomachus of Gerasa ( ).
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