Sum of Sequence of Cubes/Examples/225

From ProofWiki
Jump to navigation Jump to search

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

\(\ds 225\) \(=\) \(\ds 15^2\)
\(\ds \) \(=\) \(\ds \paren {\dfrac {5 \times \paren {5 + 1}^2} 2}^2\)
\(\ds \) \(=\) \(\ds 1 + 8 + 27 + 64 + 125\)
\(\ds \) \(=\) \(\ds 1^3 + 2^3 + 3^3 + 4^3 + 5^3\)

$\blacksquare$