Three uniform small smooth spheres \(A, B\) and \(C\) have equal radii and masses \(m, k m\) and \(m\) respectively, where \(k\) is a constant. The spheres are moving in the same direction along a straight line on a smooth horizontal surface, with \(B\) between \(A\) and \(C\). The speeds of \(A, B\) and \(C\) are \(2 u, u\) and \(\frac{4}{3} u\) respectively. The coefficient of restitution between any pair of the spheres is \(\frac{1}{2}\). After sphere \(A\) has collided with sphere \(B\), sphere \(B\) collides with sphere \(C\).
(i) Find an inequality satisfied by \(k\).

(ii) Given that \(k=2\), show that after \(B\) has collided with \(C\) there are no further collisions between any of the three spheres.