Show that \(\frac { 1 } { 5 r - 2 } - \frac { 1 } { 5 r + 3 } = \frac { A } { ( 5 r - 2 ) ( 5 r + 3 ) }\), stating the value of the constant \(A\).
(2 marks)
Hence use the method of differences to show that
$$\sum _ { r = 1 } ^ { n } \frac { 1 } { ( 5 r - 2 ) ( 5 r + 3 ) } = \frac { n } { 3 ( 5 n + 3 ) }$$
Find the value of
$$\sum _ { r = 1 } ^ { \infty } \frac { 1 } { ( 5 r - 2 ) ( 5 r + 3 ) }$$
(1 mark)