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Series convergence problem

  • Thread starter lukatwo
  • Start date
  • #1
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Homework Statement



So I need to determine if the series [itex]\Sigma[/itex][itex]ln(1+e^{-n})/n[/itex] converges.


Homework Equations





The Attempt at a Solution



I know it does, but cannot prove it. Wolfram says that the ratio test indicates that the series converges, but when I try to solve the limit I get that it equals 1(which is not conclusive). here
 
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Answers and Replies

  • #2
HallsofIvy
Science Advisor
Homework Helper
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Do you mean
[tex]\sum \frac{ln(1+ e^n}{n}[/tex]
 
  • #3
Dick
Science Advisor
Homework Helper
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Homework Statement



So I need to determine if the series [itex]\Sigma[/itex][itex]ln(1+e^-n)/n[/itex] converges.


Homework Equations





The Attempt at a Solution



I know it does, but cannot prove it. Wolfram says that the ratio test indicates that the series converges, but when I try to solve the limit I get that it equals 1(which is not conclusive). here
The series you posted looks like ln(1+e^(-n))/n. The series you tested in Mathematics looks like ln(1+e^(1/n))/n. e^(-n) is pretty different from e^(1/n).
 
  • #4
24
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No it's -n alright, but I've been switching them up along the way. Now I see my problem. Thanks
 

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