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I am having difficulty determining whether or not the following sequence can be classified as convergent or divergent:

[tex]^{\infty}_{k=1}{\sum}[/tex][tex]\frac{1}{k^{ln(k)}}[/tex]

This can be simplified to:

[tex]^{\infty}_{k=1}{\sum}[/tex][tex]\frac{1}{e^{{ln(k)}^{2}}}[/tex]

Both the ratio test and root test are inconclusive (giving values of 1), while attempting the integral test doesn't work as I am unable to integrate this as a function.

Any suggestions?

[tex]^{\infty}_{k=1}{\sum}[/tex][tex]\frac{1}{k^{ln(k)}}[/tex]

This can be simplified to:

[tex]^{\infty}_{k=1}{\sum}[/tex][tex]\frac{1}{e^{{ln(k)}^{2}}}[/tex]

Both the ratio test and root test are inconclusive (giving values of 1), while attempting the integral test doesn't work as I am unable to integrate this as a function.

Any suggestions?

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