I'll give a couple of very nitpicking remarks.
One should say, "Let s be such that for all n". Here, again, one has to describe why such s exists. And, in fact, it does not have to: consider . In general, a set of real numbers bounded from below always has an infimum but does not always have a minimum (which by definition has to be an element of the set). This is an essential point of this problem.
It's not clear to me what is. Also, if such y exists, why is it positive, as required by the question?For ,
In there exists a number y such that for all n.
A correct way is to find N such that, say, for all n > N. Then the initial segment is finite, and finite sets have not only infimum but minimum as well. Then you can find the positive lower bound for all .
For (ii), try to find an upper bound on in terms of , B, and .