Suppose that a sequence (xn) satisfies the following inequality:

abs(xn+1 - xn) < abs(xn - xn-1) for n = 2,3,4,.....

Does this sequence converge or is there a counterexample for it being divergent? If it converges, how would you prove it?

I would love some help on this particular problem. I'm not really sure if it converges or not. Thanks.