Edexcel F2 2014 June — Question 1

Exam BoardEdexcel
ModuleF2 (Further Pure Mathematics 2)
Year2014
SessionJune
TopicSequences and series, recurrence and convergence

  1. (a) Show that
$$\frac { 1 } { ( r + 1 ) ( r + 2 ) ( r + 3 ) } \equiv \frac { 1 } { 2 ( r + 1 ) ( r + 2 ) } - \frac { 1 } { 2 ( r + 2 ) ( r + 3 ) }$$ (b) Hence, or otherwise, find $$\sum _ { r = 1 } ^ { n } \frac { 1 } { ( r + 1 ) ( r + 2 ) ( r + 3 ) }$$ giving your answer as a single fraction in its simplest form.