Sum of Sequence of Cubes/Examples/36
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Examples of Sum of Sequence of Cubes
- $36 = 1^3 + 2^3 + 3^3 = 6^2 = \paren {1 + 2 + 3}^2$
Proof
| \(\ds 36\) | \(=\) | \(\ds 6^2\) | ||||||||||||
| \(\ds \) | \(=\) | \(\ds \paren {\dfrac {3 \times \paren {3 + 1}^2} 2}^2\) | ||||||||||||
| \(\ds \) | \(=\) | \(\ds 1 + 8 + 27\) | ||||||||||||
| \(\ds \) | \(=\) | \(\ds 1^3 + 2^3 + 3^3\) |
$\blacksquare$
Sources
- 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $36$
- 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $36$