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

- Oct 8th 2009, 04:40 PMbinkypoo[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, 04:46 PMNonCommAlg
- Oct 9th 2009, 07:23 AMHallsofIvy
Let $\displaystyle x_n= \sum_{k= 1}^n \frac{1}{k}$.

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