AQA FP2 2008 January — Question 2

Exam BoardAQA
ModuleFP2 (Further Pure Mathematics 2)
Year2008
SessionJanuary
TopicSequences and series, recurrence and convergence
2
  1. Show that $$( 2 r + 1 ) ^ { 3 } - ( 2 r - 1 ) ^ { 3 } = 24 r ^ { 2 } + 2$$
  2. Hence, using the method of differences, show that $$\sum _ { r = 1 } ^ { n } r ^ { 2 } = \frac { 1 } { 6 } n ( n + 1 ) ( 2 n + 1 )$$
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