AQA FP2 2006 June — Question 1

Exam BoardAQA
ModuleFP2 (Further Pure Mathematics 2)
Year2006
SessionJune
TopicSequences and series, recurrence and convergence

1
  1. Given that $$\frac { r ^ { 2 } + r - 1 } { r ( r + 1 ) } = A + B \left( \frac { 1 } { r } - \frac { 1 } { r + 1 } \right)$$ find the values of \(A\) and \(B\).
  2. Hence find the value of $$\sum _ { r = 1 } ^ { 99 } \frac { r ^ { 2 } + r - 1 } { r ( r + 1 ) }$$