Convergence of Power Series: Calculating Endpoints and Using Tests

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The discussion focuses on determining the convergence of the series summation from n=0 to infinity of (-1)^n/10. Participants suggest using the alternating series test to evaluate the endpoints of the interval of convergence. There is confusion regarding the application of the test, particularly about the behavior of the sequence bn=1/10. One participant argues that the series does not converge since the terms do not approach zero. The conversation highlights the importance of correctly applying convergence tests to series.
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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


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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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