Sum of Sequence of Cubes/Examples/225
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Examples of Sum of Sequence of Cubes
- $225 = 1^3 + 2^3 + 3^3 + 4^3 + 5^3 = 15^2 = \paren {1 + 2 + 3 + 4 + 5}^2$
Proof
\(\ds 225\) | \(=\) | \(\ds 15^2\) | ||||||||||||
\(\ds \) | \(=\) | \(\ds \paren {\dfrac {5 \times \paren {5 + 1}^2} 2}^2\) | ||||||||||||
\(\ds \) | \(=\) | \(\ds 1 + 8 + 27 + 64 + 125\) | ||||||||||||
\(\ds \) | \(=\) | \(\ds 1^3 + 2^3 + 3^3 + 4^3 + 5^3\) |
$\blacksquare$