2. (a) Write \(\frac { 3 r + 1 } { r ( r - 1 ) ( r + 1 ) }\) in partial fractions.
(b) Hence find $$\sum _ { r = 2 } ^ { n } \frac { 3 r + 1 } { r ( r - 1 ) ( r + 1 ) } \quad n \geqslant 2$$ giving your answer in the form $$\frac { a n ^ { 2 } + b n + c } { 2 n ( n + 1 ) }$$ where \(a\), \(b\) and \(c\) are integers to be determined.
(c) Hence determine the exact value of $$\sum _ { r = 15 } ^ { 20 } \frac { 3 r + 1 } { r ( r - 1 ) ( r + 1 ) }$$