Problem understanding divergence test

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    Divergence Test
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The discussion revolves around the application of the preliminary divergence test for infinite series that include both positive and negative terms. Participants clarify that the divergence test states if the limit of a_n as n approaches infinity is not zero, the series diverges, while if it approaches zero, the test is inconclusive. There is confusion regarding the inclusion of negative terms in the series, with a consensus that negative terms can exist but must be handled carefully. The need for specificity in the problem statement is emphasized to provide accurate assistance. Overall, the conversation highlights the complexities of applying divergence tests to series with varying term signs.
Kolahal Bhattacharya
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I am going through Boas.Ch-1.on infinite series.
Can anyone help?
1.May we use preliminary divergence test for series with +ve and -ve terms?How?For some situation occurs when we are supposed to make out (-1)^infinity
 
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I am sorry, but you are going to need to be a little more specific about your problem. Recall from your Calculus courses that there a number of different divergence/convergence tests for infinite series.
 
Re divergence test

It says limit a#n as n tends to infinity when not equal to zero, the series diverges.And as a#n tends to zero as n tends to infinity is inconclusive.I want to know, whether a#n may be negative numbers.
 
Infinite series use n to denote the number of the term in the series, you cannot of a 'negative' term (that I know of) in a series. I am not even sure what you are asking though.
 

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