Show that, for \(r > 0\),
$$\ln ( r + 2 ) - \ln r = \ln \left( 1 + \frac { 2 } { r } \right)$$
9
Hence, using the method of differences, show that
$$\sum _ { r = 1 } ^ { n } \ln \left( 1 + \frac { 2 } { r } \right) = \ln \left( \frac { 1 } { 2 } ( n + a ) ( n + b ) \right)$$
where \(a\) and \(b\) are integers to be found.