9. (a) Given that \(A _ { r } = \frac { 1 } { r + 1 } - \frac { 2 } { r + 2 } + \frac { 1 } { r + 3 }\), show that \(A _ { r }\) can be expressed as \(\frac { 2 } { ( r + 1 ) ( r + 2 ) ( r + 3 ) }\).
(b) Hence, show that \(\sum _ { r = 1 } ^ { n } \frac { 2 } { ( r + 1 ) ( r + 2 ) ( r + 3 ) } = \frac { 1 } { 6 } - \frac { 1 } { ( n + 2 ) ( n + 3 ) }\).
(c) Find the ratio of \(\sum _ { r = 1 } ^ { 5 } A _ { r } : \sum _ { r = 1 } ^ { 10 } A _ { r }\), giving your answer in its simplest form.