\(5 \quad\) Let \(S_{N}=\sum_{r=1}^{N}(5 r+1)(5 r+6)\) and \(T_{N}=\sum_{r=1}^{N} \frac{1}{(5 r+1)(5 r+6)}\).
(i) Use standard results from the List of Formulae (MF10) to show that
\(S_{N}=\frac{1}{3} N\left(25 N^{2}+90 N+83\right)\)

(ii) Use the method of differences to express \(T_{N}\) in terms of \(N\).

monisinatin
(iii) Find \(\lim _{N \rightarrow \infty}\left(N^{-3} S_{N} T_{N}\right)\).