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.
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]