1) \text { (i) Show that } \frac{1}{r}-\frac{1}{r+2} \equiv \frac{2}{r(r+2)} \text { . } (ii) Hence find an expression, in terms of n, for \sum_{r=1}^{n} \frac{2}{r(r+2)} \text { (iii) Given

that } \sum_{r=N+1}^{\infty} \frac{2}{r(r+2)}=\frac{11}{30}, \text { find the value of } N \text { . }