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Does this series converge?

[tex]{\sum\limits_{n = 1}^\infty {\left[ {\left( {\sum\limits_{k = 1}^n {\frac{1}{k}} } \right)^{ - 1} } \right]} } [/tex]

Does this series converge?

[tex]{\sum\limits_{n = 1}^\infty {\left[ {\left( {\sum\limits_{k = 1}^n {k!} } \right)^{ - 1} } \right]} } [/tex]

**I would appreciate any help

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# Convergent Series?

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