4 (a) By first expressing \(\frac{1}{r^{2}-1}\) in partial fractions, show that
\(\sum_{r=2}^{n} \frac{1}{r^{2}-1}=\frac{3}{4}-\frac{a n+b}{2 n(n+1)},\)
where \(a\) and \(b\) are integers to be found.

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

(c) Find the limit, as \(n \rightarrow \infty\), of \(\sum_{r=n+1}^{2 n} \frac{n}{r^{2}-1}\).