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

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Homework Help Overview

The discussion revolves around the convergence of the series given by the summation of n/ln(n) from n=1 to infinity, with a focus on the application of the Ratio and Comparison tests.

Discussion Character

  • Exploratory, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • Participants explore the validity of different approaches to determine convergence, including the Ratio test and the Divergence test. Questions arise regarding the correctness of logarithmic manipulations and assumptions made during the application of these tests.

Discussion Status

There is an ongoing examination of the methods used, with some participants questioning the assumptions related to logarithmic expressions. Guidance has been offered regarding the application of the Divergence test, suggesting a potential direction for further exploration.

Contextual Notes

Participants note confusion surrounding logarithmic properties and the implications of limits as n approaches infinity. The original poster expresses uncertainty about their approach and seeks clarification on the correctness of their reasoning.

rickyram
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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?
 
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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 got to 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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