5. (a) Using the formulae for \(\sum _ { r = 1 } ^ { n } r\) and \(\sum _ { r = 1 } ^ { n } r ^ { 2 }\), show that $$\sum _ { r = 1 } ^ { n } ( r + 1 ) ( r + 5 ) = \frac { n } { 6 } ( n + 7 ) ( 2 n + 7 )$$ for all positive integers \(n\).
(b) Hence show that $$\sum _ { r = n + 1 } ^ { 2 n } ( r + 1 ) ( r + 5 ) = \frac { 7 n } { 6 } ( n + 1 ) ( a n + b )$$ where \(a\) and \(b\) are integers to be determined.