1. Looking for a Sequence

Hello! Can you show me a Sequence where a_n+1 -a_n -->0 but it is not a Cauchy-sequence?
Thank you!

2. Re: Looking for a Sequence

Originally Posted by gotmejerry
Hello! Can you show me a Sequence where a_n+1 -a_n -->0 but it is not a Cauchy-sequence?
Thank you!
The harmonic series is not Cauchy (since it does not converge), now check on what happens to $a_{n+1}-a_n$ for the harmonic series.

CB