(a) Use the method of differences to find \(\sum_{r=1}^{n} \frac{5k}{(5r+k)(5r+5+k)}\) in terms of \(n\) and \(k\), where \(k\) is a positive constant.

It is given that \(\sum_{r=1}^{\infty} \frac{5k}{(5r+k)(5r+5+k)} = \frac{1}{3}\).

(b) Find the value of \(k\).

(c) Hence find \(\sum_{r=n}^{n^2} \frac{5k}{(5r+k)(5r+5+k)}\) in terms of \(n\).