Leave $ M = (0, ∞) $ be supplied with the metric function $ d (x, y) = | tan ^ -1 (x) -tan ^ -1 (y) | $ and let {n} be from n = 1 to ∞ a sequence of positive integers.

a) Is the sequence a Cauchy sequence in (M, d)?

b) Is the sequence a convergent sequence in (M, d)?

I'm pretty sure it's Cauchy but it's not convergent, but I'm not sure how to show it.

Any help would be greatly appreciated.