Suppose that is a sequence of real numbers that converges to and that all and are non-zero.

(i) Prove that there is a positive number that for all n.

(ii)Using part (i), prove that converges to

OK, so here is how I did part (i):

Let be the smallest absolute value in the given sequence, i.e.

For ,

In there exists a number y such that for all n.

(ii) [I have no idea how to do this one -- or even that the first part is right. So any help will be greatly appreciated. Thanks in advance]