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

**binkypoo** · October 8th 2009, 04:40 PM

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

**NonCommAlg** · October 8th 2009, 04:46 PM

Originally Posted by binkypoo

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

$a_n=\ln n.$

**HallsofIvy** · October 9th 2009, 07:23 AM

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.

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

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