convergence and divergence

**featherbox** · March 1st 2010, 12:46 PM

Why is the inverse of a convergent series divergent?
Is it because it is comparable to $\sum_{n=1}^\infty \frac{1}{n}$ ?

**chisigma** · March 1st 2010, 01:03 PM

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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