Use the method of differences to find \(\sum _ { \mathrm { r } = 1 } ^ { \mathrm { n } } \frac { 1 } { ( \mathrm { kr } + 1 ) ( \mathrm { kr } - \mathrm { k } + 1 ) }\) in terms of \(n\) and \(k\), where \(k\) is a positive constant.
Deduce the value of \(\sum _ { \mathrm { r } = 1 } ^ { \infty } \frac { 1 } { ( \mathrm { kr } + 1 ) ( \mathrm { kr } - \mathrm { k } + 1 ) }\).
Find also \(\sum _ { \mathrm { r } = \mathrm { n } } ^ { \mathrm { n } ^ { 2 } } \frac { 1 } { ( \mathrm { kr } + 1 ) ( \mathrm { kr } - \mathrm { k } + 1 ) }\) in terms of \(n\) and \(k\).