Does the series Σln(1+e^-n)/n converge?

[lukatwo]

Homework Statement

So I need to determine if the series $\Sigma$$ln(1+e^{-n})/n$ 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

 

[HallsofIvy]

Do you mean
$$\sum \frac{ln(1+ e^n}{n}$$

 

[Dick]

Homework Statement

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

 

[lukatwo]

No it's -n alright, but I've been switching them up along the way. Now I see my problem. Thanks