privetek
determine whether the series converges or diverges:



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privetek
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\[\sum_{1}^{\infty} (lnk)/(e ^{\sqrt{k}})\]

EarthCitizen
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0

privetek
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what test did you use?

EarthCitizen
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when u find the limiting value \[U_{k+1}/U_{n}\]

EarthCitizen
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\[\left U _{k+1}/U_{k} \right\]

privetek
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can you kinda show me how you got zero?

EarthCitizen
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\[ U_{k} = \ln(k)/e^{k} , U_{k+1} = \ln(k+1)/e^{k+1} \]\[ \therefore \left U_{k+1}/U_{k} \right = \ln(k+1)/e^{k+1} \times e^{k}/\ln(k)\]

EarthCitizen
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\[ \ln(1) \times e^{\sqrt(k)\sqrt(k+1)} = 0\]

EarthCitizen
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did that help ?

privetek
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great! thanks :)

EarthCitizen
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what was the answer in the text book ?

privetek
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it wasn't from my textbook so i don't know the right answer but that looks right.