What did i do wrong? Ratio and comparison test question? (1 Viewer)

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1. The problem statement, all variables and given/known data

The summation of n/lnn from n=1 to infinity

2. Relevant equations

Ratio and Comparison test


3. The attempt at a solution

http://i55.tinypic.com/2jxuue.jpg

Alright so the way labeled "right way" on the picture is the right way according to the book but isn't the way I did with the ratio test right also? What did i do wrong?
 
It is NOT true that

[tex]\frac{ln(n+1)}{ln(n)}=ln(1) [/tex]
 
ln (n+1) / ln (n) isn't ln(1), in the limit or otherwise.
 
Oh man, I gotta brush up on my logarithm rules... Anyway thanks for answerin my question, it has been a big help.
 
Apply the divergence test directly. take limit n->(infinity) n/lnn. I doubt that goes to zero!
 

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