5 The roots of the cubic equation \(x ^ { 3 } + 3 x ^ { 2 } - 7 x + 1 = 0\) are \(\alpha , \beta\) and \(\gamma\). Find the cubic equation whose roots are \(3 \alpha , 3 \beta\) and \(3 \gamma\), expressing your answer in a form with integer coefficients.
- Show that \(\frac { 1 } { r + 2 } - \frac { 1 } { r + 3 } = \frac { 1 } { ( r + 2 ) ( r + 3 ) }\).
- Hence use the method of differences to find \(\frac { 1 } { 3 \times 4 } + \frac { 1 } { 4 \times 5 } + \frac { 1 } { 5 \times 6 } + \ldots + \frac { 1 } { 52 \times 53 }\).