# Real analysis – Checking if a sequence is Cauchy and / or convergent.

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.