Key identity
The cube series satisfies sum_{k=1}^{n}k^3=left( rac{n(n+1)}{2} ight)^2.
That means the sum of cubes is always the square of the nth triangular number.
Useful checks
- Verifying algebra practice and induction examples.
- Comparing a direct sum with the compact formula.
- Recognizing how quickly higher powers grow.
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