2 (a) Use standard results from the List of Formulae (MF19) to show that
\(\sum_{r=1}^{n}(7 r+1)(7 r+8)=a n^{3}+b n^{2}+c n\)
where \(a, b\) and \(c\) are constants to be determined.

(b) Use the method of differences to find \(\sum_{r=1}^{n} \frac{1}{(7 r+1)(7 r+8)}\) in terms of \(n\).

(c) Deduce the value of \(\sum_{r=1}^{\infty} \frac{1}{(7 r+1)(7 r+8)}\).