Let \(a\) be a positive constant.

(a) Use the method of differences to find \(\sum_{r=1}^{n} \frac{1}{(ar+1)(ar+a+1)}\) in terms of \(n\) and \(a\).

(b) Find the value of \(a\) for which \(\sum_{r=1}^{\infty} \frac{1}{(ar+1)(ar+a+1)} = \frac{1}{6}\).