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Please suggest a most simple sequence with the following properties:

$$\sum_{n=1}^{\infty} a_n=1$$

$$\frac1{a_n} \sim n!$$

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    I don't know what $\sim$ means here; could you edit the question to explain what you're looking for? It seems like the solution is trivial, because $\sum_{n=1}^\infty 1/(n!)$ converges.2011-04-10
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    It means $(1/a_n)/n! \to 1$ as $n \to \infty$.2011-04-10
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    At least it should mean that, according to standard notation. @Annix: What exactly $\sim$ means here?2011-04-10

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