Does the Series Converge or Diverge?

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Homework Help Overview

The discussion revolves around determining the convergence or divergence of an infinite series, specifically the series \(\sum^{∞}_{k=1} \frac{k-3}{k}\). Participants are exploring the implications of the test for divergence and considering other tests for convergence.

Discussion Character

  • Conceptual clarification, Assumption checking, Mixed

Approaches and Questions Raised

  • Participants are examining the limit of the series and its implications for convergence. There is confusion regarding the application of the test for divergence, with some questioning the original poster's conclusions about convergence and divergence.

Discussion Status

The discussion is active, with participants providing hints and questioning assumptions. There is a recognition that the series diverges based on the limit not being equal to zero, and suggestions to consider a comparison test have been made.

Contextual Notes

Participants are navigating the nuances of convergence tests and are addressing potential contradictions in reasoning. The original poster's understanding of the test for divergence is under scrutiny, indicating a need for clarity on the conditions for convergence.

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Homework Statement


Determine whether the infinite series converges or divergens. If it converges find its sum.
\sum^{∞}_{k=1} \frac{k-3}{k}


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The Attempt at a Solution



I found the limit and realized that the limit is 1. So I said that the series converges by the test for divergence. And since it diverges I don't have to worry about finding a sum.


However, I'm not sure if I'm using the test for divergence right.
 
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I'm Awesome said:


I found the limit and realized that the limit is 1. So I said that the series converges by the test for divergence. And since it diverges I don't have to worry about finding a sum.



You are contradicting yourself. Do you think it converges or diverges ?

Hint: This series doesn't converge try and use a comparison test too see why.
 
sid9221 said:
You are contradicting yourself. Do you think it converges or diverges ?

Hint: This series doesn't converge try and use a comparison test too see why.

Sorry, I ment to say that the series diverges by the test for divergence because the limit is not equal to 0.
 
Yes, by the non null test is this is divergent as the limit is not equal to zero.
 

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