Edexcel CP2 2021 June — Question 4

Exam BoardEdexcel
ModuleCP2 (Core Pure 2)
Year2021
SessionJune
TopicSequences and series, recurrence and convergence

  1. In this question you may assume the results for
$$\sum _ { r = 1 } ^ { n } r ^ { 3 } , \sum _ { r = 1 } ^ { n } r ^ { 2 } \text { and } \sum _ { r = 1 } ^ { n } r$$
  1. Show that the sum of the cubes of the first \(n\) positive odd numbers is $$n ^ { 2 } \left( 2 n ^ { 2 } - 1 \right)$$ The sum of the cubes of 10 consecutive positive odd numbers is 99800
  2. Use the answer to part (a) to determine the smallest of these 10 consecutive positive odd numbers.