What did i do wrong? Ratio and comparison test question?

[rickyram]

Homework Statement

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

Homework Equations

Ratio and Comparison test

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?

 

[micromass]

It is NOT true that

$$\frac{ln(n+1)}{ln(n)}=ln(1)$$

 

[hgfalling]

ln (n+1) / ln (n) isn't ln(1), in the limit or otherwise.

 

[rickyram]

Oh man, I got to brush up on my logarithm rules... Anyway thanks for answerin my question, it has been a big help.

 

[╔(σ_σ)╝]

Apply the divergence test directly. take limit n->(infinity) n/lnn. I doubt that goes to zero!