2 Let \(u_{n}=\frac{4 \sin \left(n-\frac{1}{2}\right) \sin \frac{1}{2}}{\cos (2 n-1)+\cos 1}\).
(i) Using the formulae for \(\cos P \pm \cos Q\) given in the List of Formulae MF10, show that
\(u_{n}=\frac{1}{\cos n}-\frac{1}{\cos (n-1)}\)
(ii) Use the method of differences to find \(\sum_{n=1}^{N} u_{n}\).

(iii) Explain why the infinite series \(u_{1}+u_{2}+u_{3}+\ldots\) does not converge.