5 The sum to \(r\) terms, \(S _ { r }\), of a series is given by
$$S _ { r } = r ^ { 2 } ( r + 1 ) ( r + 2 )$$
Given that \(u _ { r }\) is the \(r\) th term of the series whose sum is \(S _ { r }\), show that:
- \(u _ { 1 } = 6\);
- \(u _ { 2 } = 42\);
- \(\quad u _ { n } = n ( n + 1 ) ( 4 n - 1 )\).
- Show that
$$\sum _ { r = n + 1 } ^ { 2 n } u _ { r } = 3 n ^ { 2 } ( n + 1 ) ( 5 n + 2 )$$