hint: to think about b and c, consider the sequence 1/2, 1/3, 1/4, 1/5, 1/6, 1/7, ...
plugging in more and more terms of that sequence into your sum, what do you get? It should look like a familiar series from a calculus course. Can that series converge? (Hint: is the general term going to zero?)
To think about a, plug in the sequence 1, 2, 3, 4, ... Does that sum converge? That's all the natural numbers, so if that sum converges, then you win.
EDIT: in each case, we have an infinite series that either diverges or converges. So to express this in terms of finite sets $B$, pick finite sets $B_n$ that exhaust my sequence, e.g. in the example with b and c, look at $B = \{1/2\}$, then $B = \{1/2, 1/3\}$, then $B = \{1/2, 1/3, 1/4\}$, then $\ldots$. The supremum over all the sets $B$ will be (at least as large as) the sum of the infinite series since we can pick $B$ containing as many of the terms of the infinite series as we like.