Question 1 - A-Level Maths

Exam Board	OCR MEI
Module	Further Pure Core (Further Pure Core)
Year	2022
Session	June
Topic	Sequences and series, recurrence and convergence

By considering \(( r + 1 ) ^ { 3 } - r ^ { 3 }\), find \(\sum _ { \mathrm { r } = 1 } ^ { \mathrm { n } } \left( 3 \mathrm { r } ^ { 2 } + 3 \mathrm { r } + 1 \right)\).
Use this result to find \(\sum _ { r = 1 } ^ { n } r ( r + 1 )\), expressing your answer in fully factorised form.