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

  1. #1
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    [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
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  2. #2
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    Quote Originally Posted by binkypoo View Post

    Hi I need an example of the sequence described in the title any help? Thanks
    a_n=\ln n.
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    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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