4 (i) Use the method of differences to show that \(\sum_{r=1}^{N} \frac{1}{(3 r+1)(3 r-2)}=\frac{1}{3}-\frac{1}{3(3 N+1)}\).

(ii) Find the limit, as \(N \rightarrow \infty\), of \(\sum_{r=N+1}^{N^{2}} \frac{N}{(3 r+1)(3 r-2)}\).