d($y(n),y(n+1)$)$<=1/n$ then is {$y(n)$} a Cauchy Sequence? d($y(n),y(n+1)$)$<=1/n^2$, then is {$y(n)$} Cauchy?

Question

Let {$y(n)$} be a sequence in a complete metric space (X,d) such that d($y(n),y(n+1)$)$<=1/n$. Give any example of such a sequence {$y(n)$} which is not Cauchy. If we take d($y(n),y(n+1)$)$<=1/n^2$, then is {$y(n)$} Cauchy?