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Want the Series converges, and its sum, if there is

Evaluate ` sum_(n=2)^(infty)sqrt(n)/(ln(n)) `


This series does not converge.


If the series converges, then the limit of its nth term must be 0 as n grows without bound. Using L'Hopital's rule we show that the limit does not exist:


`lim_(n->oo)sqrt(n)/(ln(n))=lim_(n->oo)(1/(2sqrt(n)))/(1/n) `


`=lim_(n->oo)n/(2sqrt(n))=lim_(n->oo)(sqrt(n))/(2) = oo `

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