Edexcel F1 2015 January — Question 7

Exam BoardEdexcel
ModuleF1 (Further Pure Mathematics 1)
Year2015
SessionJanuary
TopicSequences and series, recurrence and convergence

7. Given that, for all positive integers \(n\), $$\sum _ { r = 1 } ^ { n } ( r + a ) ( r + b ) = \frac { 1 } { 6 } n ( 2 n + 11 ) ( n - 1 )$$ where \(a\) and \(b\) are constants and \(a > b\),
  1. find the value of \(a\) and the value of \(b\).
  2. Find the value of $$\sum _ { r = 9 } ^ { 20 } ( r + a ) ( r + b )$$