5 (i) Show that

$$\frac { r + 1 } { r + 2 } - \frac { r } { r + 1 } = \frac { 1 } { ( r + 1 ) ( r + 2 ) }$$

(ii) Hence find an expression, in terms of $n$, for

$$\frac { 1 } { 6 } + \frac { 1 } { 12 } + \frac { 1 } { 20 } + \ldots + \frac { 1 } { ( n + 1 ) ( n + 2 ) }$$

(iii) Hence write down the value of $\sum _ { r = 1 } ^ { \infty } \frac { 1 } { ( r + 1 ) ( r + 2 ) }$.

\hfill \mbox{\textit{OCR FP1  Q5}}