Convergence of Power Series: Calculating Endpoints and Using Tests

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Homework Help Overview

The discussion revolves around the convergence of a power series, specifically focusing on calculating the endpoints of a known interval of convergence. The original poster is questioning whether the series summation from n=0 to infinity of (-1)^n/10 converges or diverges, and is seeking clarification on applicable tests for convergence.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • Participants discuss the use of the alternating series test and question the convergence of the series in question. The original poster expresses confusion regarding the outcome of the test and the implications of the series terms.

Discussion Status

The discussion is ongoing, with participants exploring different interpretations of the series' behavior. Some guidance has been offered regarding the alternating series test, but there is no clear consensus on the convergence of the series itself.

Contextual Notes

There appears to be some confusion regarding the terms of the series and their implications for convergence, as well as the application of the alternating series test. The original poster's understanding of the series' behavior is under scrutiny.

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Homework Statement


I'm having a little trouble concerning the part where we have to calculate the endpoints of a known interval of convergence in order to see whether they are convergent or divergent. In this case, is the summation of n=0 to infinity of (-1)^n/10 diverging or converging. Are there any tests to prove that? I'm kinda confused. Thanks


Homework Equations





The Attempt at a Solution

 
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Have you looked at the alternating series test?
 
Mark44 said:
Have you looked at the alternating series test?

uhh yea, but it just gives bn= 1/10 which doesn;t make sense...i think
 
(-1)^n/10 doesn't converge. Don't be silly. It doesn't even approach 0. Did you mean to post something else?
 

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