Question 1 - A-Level Maths

Exam Board	Edexcel
Module	FP2 (Further Pure Mathematics 2)
Year	2004
Session	June
Topic	Sequences and series, recurrence and convergence

Show that \(( r + 1 ) ^ { 3 } - ( r - 1 ) ^ { 3 } \equiv A r ^ { 2 } + B\), where \(A\) and \(B\) are constants to be found.
Prove by the method of differences that \(\sum _ { r = 1 } ^ { n } r ^ { 2 } = \frac { 1 } { 6 } n ( n + 1 ) ( 2 n + 1 ) , n > 1\).
(6)(Total 8 marks)