Convergence of Series: Proving and Finding the Sum

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Homework Help Overview

The discussion revolves around proving the convergence of a series and finding its sum. Participants are exploring various series tests and theorems related to convergence in the context of series analysis.

Discussion Character

  • Exploratory, Assumption checking, Conceptual clarification

Approaches and Questions Raised

  • Participants are discussing different series tests, such as the ratio test and divergence test, and questioning which tests are applicable to the series in question. There is an exploration of the criteria for these tests and their effectiveness in proving convergence.

Discussion Status

The discussion is ongoing, with participants attempting to identify suitable tests for convergence. Some guidance has been offered regarding specific tests, but there is no explicit consensus on which test to apply or its effectiveness.

Contextual Notes

There appears to be some confusion regarding the application of series tests, and participants are expressing uncertainty about how to proceed with proving convergence. The original poster has indicated a desire for assistance but has not received direct responses.

aleebai
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prove the convergence of the series and find the sum.

please help me
 

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What series tests do you know?
 
R136a1 said:
What series tests do you know?

i don't understand your question /
 
aleebai said:
i don't understand your question /

What theorems or results do you know that allow you to (dis)prove convergence?

For example, you have the ratio test. Or you have the divergence test that allow you to show convergence if the terms of the series do not converge to ##0##.

So, which of these tests do you know?
 
R136a1 said:
What theorems or results do you know that allow you to (dis)prove convergence?

For example, you have the ratio test. Or you have the divergence test that allow you to show convergence if the terms of the series do not converge to ##0##.

So, which of these tests do you know?

sign Leibniz , Dalambers
 
aleebai said:
sign Leibniz , Dalambers

OK, so try those tests. Are there any that work?
 
R136a1 said:
OK, so try those tests. Are there any that work?

that's it I can not decide =) wanted to ask for help, but sorry no one answers.
 
aleebai said:
that's it I can not decide =) wanted to ask for help, but sorry no one answers.

Pick some test that you know, and try it! If it doesn't work, try another one.

Let's start with the first one you mentioned: the sign test, what does that say? Does this series satisfy the criteria?
 

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