- Given that
$$\frac { 2 n + 1 } { n ^ { 2 } ( n + 1 ) ^ { 2 } } \equiv \frac { A } { n ^ { 2 } } + \frac { B } { ( n + 1 ) ^ { 2 } }$$
- determine the value of \(A\) and the value of \(B\)
- Hence show that, for \(n \geqslant 5\)
$$\sum _ { r = 5 } ^ { n } \frac { 2 r + 1 } { r ^ { 2 } ( r + 1 ) ^ { 2 } } = \frac { n ^ { 2 } + a n + b } { c ( n + 1 ) ^ { 2 } }$$
where \(a\), \(b\) and \(c\) are integers to be determined.