2. (a) Show that, for \(r > 0\) $$r - 3 + \frac { 1 } { r + 1 } - \frac { 1 } { r + 2 } = \frac { r ^ { 3 } - 7 r - 5 } { ( r + 1 ) ( r + 2 ) }$$ (b) Hence prove, using the method of differences, that $$\sum _ { r = 1 } ^ { n } \frac { r ^ { 3 } - 7 r - 5 } { ( r + 1 ) ( r + 2 ) } = \frac { n \left( n ^ { 2 } + a n + b \right) } { 2 ( n + 2 ) }$$ where \(a\) and \(b\) are constants to be found.