Infinitie series with ln()

[turbowaffle]

I'm not sure how to approach the following:

\(\displaystyle \Sigma\limits_{n=1}^{\infty}\ln(\frac{n}{2n+5})\)

There aren't any other problems in the book that show you how to deal with series of functions, like ln(). I'm supposed to find the value it converges to. Any ideas?

 

[stapel]

What "tests" do you have to work with? Like the "Ratio Test" and such...?

Thank you.

Eliz.

 

[Gene]

Something is wrong.
As n -> oo each term -> ln(1/2) = -.6931... so you are adding an infinite number of negative terms. No limit.

 

[turbowaffle]

Wow, I feel really dumb. I was thinking the limit of x/(2*x+5) was 1 (x over x), which would make ln(1) = 0, but you're right, the limit is 1/2, so it diverges. Don't you love it when a problem seems really complicated because of a very simple oversight? Thanks!