(a) Use standard results from the list of formulae (MF19) to show that

\(\sum_{r=1}^{n} (2-3r)(5-3r) = an^3 + bn^2 + cn,\)

where \(a, b\) and \(c\) are integers to be determined.

(b) Use the method of differences to find \(\sum_{r=1}^{n} \frac{1}{(2-3r)(5-3r)}\) in terms of \(n\).

(c) Deduce the value of \(\sum_{r=1}^{\infty} \frac{1}{(2-3r)(5-3r)}\).