Use standard results from the list of formulae (MF19) to find \(\sum _ { r = 1 } ^ { n } r ( r + 1 ) ( r + 2 )\) in terms of \(n\),
fully factorising your answer. fully factorising your answer.
Express \(\frac { 1 } { r ( r + 1 ) ( r + 2 ) }\) in partial fractions and hence use the method of differences to find
$$\sum _ { r = 1 } ^ { n } \frac { 1 } { r ( r + 1 ) ( r + 2 ) }$$
Deduce the value of \(\sum _ { r = 1 } ^ { \infty } \frac { 1 } { r ( r + 1 ) ( r + 2 ) }\).