Question 5 - A-Level Maths

Exam Board	CAIE
Module	FP1 (Further Pure Mathematics 1)
Year	2019
Session	November
Topic	Sequences and series, recurrence and convergence

Use standard results from the List of Formulae (MF10) to show that $$S _ { N } = \frac { 1 } { 3 } N \left( 25 N ^ { 2 } + 90 N + 83 \right)$$
Use the method of differences to express $T _ { N }$ in terms of $N$.
Find $\lim _ { N \rightarrow \infty } \left( N ^ { - 3 } S _ { N } T _ { N } \right)$.