I'll give a couple of very nitpicking remarks.

When one says "let x be y", usually x is a fresh variable, a new name for the described object y. If x is not just a name, but an expression, then it is not clear that the right-hand side y can have the form x. For example, consider "let (x+2)(x-1) be -2". Does such x exist, and if it does, is it unique? So, wrapping in the absolute value function, as in your case, is suspicious from the start.

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 .