(a) Use standard results from MF19 to find \(\sum_{r=1}^{n}(r^3-r)\) in terms of \(n\), fully factorising your answer.

(b) Express \(\dfrac{r+3}{r^3-r}\) in the form \(\dfrac{A}{r-1}+\dfrac{B}{r}+\dfrac{C}{r+1}\), and hence use the method of differences to find \(\sum_{r=2}^{n}\dfrac{r+3}{r^3-r}\).

(c) Deduce the value of \(\sum_{r=2}^{\infty}\dfrac{r+3}{r^3-r}\).