Show that \(r ( r + 1 ) ( r + 2 ) - ( r - 1 ) r ( r + 1 ) \equiv 3 r ( r + 1 )\).
Hence use the method of differences to find an expression for \(\sum _ { r = 1 } ^ { n } r ( r + 1 )\).
Show that you can obtain the same expression for \(\sum _ { r = 1 } ^ { n } r ( r + 1 )\) using the standard formulae for \(\sum _ { r = 1 } ^ { n } r\) and \(\sum _ { r = 1 } ^ { n } r ^ { 2 }\).