anonymous
  • anonymous
determine whether the series converges or diverges:
Mathematics
katieb
  • katieb
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anonymous
  • anonymous
\[\sum_{1}^{\infty} (lnk)/(e ^{\sqrt{k}})\]
EarthCitizen
  • EarthCitizen
0
anonymous
  • anonymous
what test did you use?

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EarthCitizen
  • EarthCitizen
when u find the limiting value \[U_{k+1}/U_{n}\]
EarthCitizen
  • EarthCitizen
\[\left| U _{k+1}/U_{k} \right|\]
anonymous
  • anonymous
can you kinda show me how you got zero?
EarthCitizen
  • EarthCitizen
\[ U_{k} = \ln(k)/e^{k} , U_{k+1} = \ln(k+1)/e^{k+1} \]\[ \therefore \left| U_{k+1}/U_{k} \right| = \ln(k+1)/e^{k+1} \times e^{k}/\ln(k)\]
EarthCitizen
  • EarthCitizen
\[ \ln(1) \times e^{\sqrt(k)-\sqrt(k+1)} = 0\]
EarthCitizen
  • EarthCitizen
did that help ?
anonymous
  • anonymous
great! thanks :)
EarthCitizen
  • EarthCitizen
what was the answer in the text book ?
anonymous
  • anonymous
it wasn't from my textbook so i don't know the right answer but that looks right.

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