# Problem understanding divergence test

• Kolahal Bhattacharya
In summary, the conversation discusses the use of the preliminary divergence test for series with positive and negative terms. It is mentioned that there are different tests for convergence and divergence in calculus. The divergence test is explained and it is stated that it cannot be used for negative terms. The speaker also asks for clarification on the problem at hand.
Kolahal Bhattacharya
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

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.

## What is the "Problem understanding divergence test"?

The problem understanding divergence test is a concept in mathematics and statistics that is used to determine the convergence or divergence of a series. It involves analyzing the behavior of the terms in a series to determine whether the series will approach a finite value (converge) or approach infinity (diverge).

## When is the divergence test used?

The divergence test is typically used when other convergence tests, such as the ratio test or the root test, are inconclusive. It is also commonly used in calculus to determine the convergence or divergence of improper integrals.

## What is the difference between absolute and conditional convergence?

Absolute convergence occurs when a series converges regardless of the order in which the terms are added. Conditional convergence, on the other hand, occurs when the series only converges if the terms are added in a specific order. The divergence test can be used to determine absolute convergence, but it cannot determine conditional convergence.

## How do you apply the divergence test?

To apply the divergence test, you need to first evaluate the limit of the terms in the series as n approaches infinity. If the limit is equal to zero, then the series may converge or diverge. If the limit is not equal to zero, then the series will diverge. However, it is important to note that if the limit is equal to zero, the series may still diverge, and further tests may be necessary to determine convergence.

## Are there any limitations to the divergence test?

Yes, the divergence test has limitations. It can only be used to determine divergence or absolute convergence. It cannot determine conditional convergence, and it is not always conclusive. Additionally, the test may not work for series that have alternating signs or terms that do not approach zero as n approaches infinity.

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