Sum of Sequence of Cubes/Examples/100
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Examples of Sum of Sequence of Cubes
- $100 = 1^3 + 2^3 + 3^3 + 4^3 = 10^2 = \left({1 + 2 + 3 + 4}\right)^2$
Proof
| \(\ds 100\) | \(=\) | \(\ds 10^2\) | ||||||||||||
| \(\ds \) | \(=\) | \(\ds \left({\dfrac {4 \times \left({4 + 1}\right)^2} 2}\right)^2\) | ||||||||||||
| \(\ds \) | \(=\) | \(\ds 1 + 8 + 27 + 64\) | ||||||||||||
| \(\ds \) | \(=\) | \(\ds 1^3 + 2^3 + 3^3 + 4^3\) |
$\blacksquare$