Question 5 - A-Level Maths

Exam Board	AQA
Module	Further AS Paper 1 (Further AS Paper 1)
Year	2020
Session	June
Marks	1
Topic	Sequences and series, recurrence and convergence

Show that $$r ^ { 2 } ( r + 1 ) ^ { 2 } - ( r - 1 ) ^ { 2 } r ^ { 2 } = p r ^ { 3 }$$ where $p$ is an integer to be found.
[0pt] [1 mark]
5
Hence use the method of differences to show that $$\sum _ { r = 1 } ^ { n } r ^ { 3 } = \frac { 1 } { 4 } n ^ { 2 } ( n + 1 ) ^ { 2 }$$