AQA FP1 2013 January — Question 8

Exam BoardAQA
ModuleFP1 (Further Pure Mathematics 1)
Year2013
SessionJanuary
TopicSequences and series, recurrence and convergence

8
  1. Show that $$\sum _ { r = 1 } ^ { n } 2 r \left( 2 r ^ { 2 } - 3 r - 1 \right) = n ( n + p ) ( n + q ) ^ { 2 }$$ where \(p\) and \(q\) are integers to be found.
  2. Hence find the value of $$\sum _ { r = 11 } ^ { 20 } 2 r \left( 2 r ^ { 2 } - 3 r - 1 \right)$$ (2 marks)