Edexcel F2 2021 June — Question 1

Exam BoardEdexcel
ModuleF2 (Further Pure Mathematics 2)
Year2021
SessionJune
TopicPartial Fractions
TypeQuadratic factor (difference of squares)

  1. (a) Express \(\frac { 2 } { r \left( r ^ { 2 } - 1 \right) }\) in partial fractions.
    (b) Hence find, in terms of \(n\),
$$\sum _ { r = 2 } ^ { n } \frac { 1 } { r \left( r ^ { 2 } - 1 \right) }$$ Give your answer in the form $$\frac { n ^ { 2 } + A n + B } { C n ( n + 1 ) }$$ where \(A\), \(B\) and \(C\) are constants to be found.