(a) Use the list of formulae (MF19) to find \(\sum_{r=1}^{n} r(r+2)\) in terms of \(n\), simplifying your answer.

(b) Express \(\frac{1}{r(r+2)}\) in partial fractions and hence find \(\sum_{r=1}^{n} \frac{1}{r(r+2)}\) in terms of \(n\).

(c) Deduce the value of \(\sum_{r=1}^{\infty} \frac{1}{r(r+2)}\).