Using ratio test to test conditional convergence?

In summary, the ratio test is a mathematical test used to determine the convergence or divergence of a series by taking the limit of the ratio of consecutive terms. It can also be used to test for conditional convergence by applying it to the absolute value of the terms in a series. The conditions for using the ratio test include having positive terms, an infinite series, and an existing limit of the ratio of consecutive terms. However, it cannot determine the exact sum of a series and may not always give a conclusive answer. Other tests may be needed for more complex series.
  • #1
theBEAST
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Homework Statement


So what I was taught was that if the lim of the ratio test is the series is always absolutely convergent. If it is >1 the series is always divergent. But if it is =1 then we don't know. So would that mean that all conditionally convergent series would have a limit = 1? I am confused :s

Thanks!
 
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  • #2
Yes, if the ratio test applied to conditional convergent series exists, then it must be 1. On the other hand, the ratio test might not give you a limit at all. In that case the series can do anything it wants to.
 

FAQ: Using ratio test to test conditional convergence?

1. What is the ratio test and how does it work?

The ratio test is a mathematical test used to determine the convergence or divergence of a series. It involves taking the limit of the ratio of consecutive terms in the series. If the limit is less than 1, the series converges; if it is greater than 1, the series diverges; and if it is equal to 1, the test is inconclusive.

2. How is the ratio test used to test for conditional convergence?

The ratio test can be used to test for conditional convergence by applying it to the absolute value of the terms in a series. If the absolute value of the terms converges, then the series is absolutely convergent and also conditionally convergent. If the absolute value of the terms diverges, then the series is not conditionally convergent.

3. What are the conditions for using the ratio test?

The ratio test can only be used for series with positive terms. Additionally, the series must be infinite and the limit of the ratio of consecutive terms must exist.

4. Can the ratio test be used to determine the exact sum of a series?

No, the ratio test can only determine the convergence or divergence of a series, it cannot determine the exact sum. Other tests, such as the geometric series test or telescoping series test, can be used to find the sum of certain types of series.

5. Are there any limitations to using the ratio test?

Yes, the ratio test may not always give a conclusive answer for certain series. In these cases, other tests may need to be used to determine convergence or divergence. Additionally, the ratio test can only be used for series with positive terms and may not work for more complex series.

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