# Thread: [SOLVED] Contracting but not converging ?

1. ## [SOLVED] Contracting but not converging ?

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

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

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!

2. Let $t_n= \sum_{j=1} ^{n} \ \frac{1}{j}$

3. Why wouldnt such a sequence be converging?

4. Originally Posted by Jose27
Let $t_n= \sum_{j=1} ^{n} \ \frac{1}{j}$
Originally Posted by tyro89
Why wouldnt such a sequence be converging?
Have you heard of the harmonic series?

5. I have now thank's a lot ! Based on what have been thaught up to now in my class this was really an odd question...