Given that
$$\frac { 1 } { r ( r + 1 ) ( r + 2 ) } = \frac { A } { r ( r + 1 ) } + \frac { B } { ( r + 1 ) ( r + 2 ) }$$
show that \(A = \frac { 1 } { 2 }\) and find the value of \(B\).
Use the method of differences to find
$$\sum _ { r = 10 } ^ { 98 } \frac { 1 } { r ( r + 1 ) ( r + 2 ) }$$
giving your answer as a rational number.