5 The first four terms of the series \(S\) can be written as
$$S = ( 1 \times 2 ) + ( 2 \times 3 ) + ( 3 \times 4 ) + ( 4 \times 5 ) + \ldots$$
5
- Write an expression, using \(\sum\) notation, for the sum of the first \(n\) terms of \(S\)
5
- Show that the sum of the first \(n\) terms of \(S\) is equal to
$$\frac { 1 } { 3 } n ( n + 1 ) ( n + 2 )$$