Let (X, d) be a metric space and let {pn} be a sequence of elements of this metric space such that d(pn+1, pn+2) d(pn, pn+1) n 1, where [0, 1). Then {pn} is a convergent sequence in (X, d). Disprove this statement by constructing a counterexample. Then formulate the correct statement and prove it.