Determining Convergence/Divergence Of Infinite Series

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Homework Help Overview

The discussion revolves around determining the convergence or divergence of an infinite series. Participants are exploring methods to analyze the series and the implications of various tests related to convergence.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • Participants discuss the divergence of the series based on initial observations of its terms. There is a focus on finding a general term for the series to facilitate analytical evaluation. Questions arise regarding the necessity of identifying a general term for proving divergence.

Discussion Status

Some participants have suggested applying a specific test as a preliminary step to assess divergence. The conversation is ongoing, with various interpretations of the series' behavior being explored.

Contextual Notes

There is mention of a simple test that should be applied first, although the specific details of this test are not fully elaborated in the discussion.

Bashyboy
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Homework Statement


I attached the solution to the problem.


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The Attempt at a Solution


I can see that the infinite series diverges by looking at a few terms, but how would I find a general term for the infinite series, to evaluate it analytically?
 

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Bashyboy said:
I can see that the infinite series diverges by looking at a few terms, but how would I find a general term for the infinite series, to evaluate it analytically?

If your goal is to prove that the series diverges, you don't necessarily need to find an expression for the general term (by which I assume you mean the n'th partial sum).

There is a very simple test which you should always apply as the first step. If this test fails, the series diverges. What test am I referring to?
 
Would it be the nth term test?
 
Yes. What does that test imply for this series?
 

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