# [SOLVED] example of a divergent sequence where lim|a_n+1 - a_n| = 0 as n goes to in

• Oct 8th 2009, 05:40 PM
binkypoo
[SOLVED] example of a divergent sequence where lim|a_n+1 - a_n| = 0 as n goes to in
Hi I need an example of the sequence described in the title any help? Thanks
• Oct 8th 2009, 05:46 PM
NonCommAlg
Quote:

Originally Posted by binkypoo

Hi I need an example of the sequence described in the title any help? Thanks

$a_n=\ln n.$
• Oct 9th 2009, 08:23 AM
HallsofIvy
Let $x_n= \sum_{k= 1}^n \frac{1}{k}$.

Then $x_{n+1}- x_n= \frac{1}{n+1}$ which goes to 0 but sequence is the partial sums for the harmonic series which does not converge.