Title says it all. I have to find a non converging sequence such that:

$\displaystyle \left| t_{n+1} - t_{n} \right| < \left| t_{n} - t_{n-1} \right| \forall n \geq 2$

I just can't seem to find any such sequence and it seems to me that the definition implies that any such sequence must be converging. Any hint/thought would be appreciated!

Thanks!