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Math Help - convergence and divergence

  1. #1
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    convergence and divergence

    Why is the inverse of a convergent series divergent?
    Is it because it is comparable to \sum_{n=1}^\infty \frac{1}{n} ?
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  2. #2
    MHF Contributor chisigma's Avatar
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    Let be a_{n} the general term of a convergent series. In this case is \lim_{n \rightarrow \infty} a_{n}=0 so that \lim_{n \rightarrow \infty} \frac{1}{a_{n}} = \pm \infty... that's why the series of the \frac{1}{a_{n}} never converges ...

    Kind regards

    \chi \sigma
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