Series Ratio Test: Answer 1/7 - Confirm?

Thread starter naspek
Start date Dec 9, 2009
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Ratio test Series Test

In summary, the Series Ratio Test is a method used to determine the convergence or divergence of a series by taking the limit of the ratio of consecutive terms. If the limit is less than 1, the series is absolutely convergent. If the limit is greater than 1, the series is divergent. A limit of 1 or non-existence of the limit requires further analysis. The test is highly accurate but can give inconclusive results, so it is important to use other methods for confirmation. The Series Ratio Test can only be applied to series with positive terms and monotonic decrease. Other methods must be used for series that do not meet these criteria.

Dec 9, 2009

naspek

Hey there.. I've done the ration test for the series at the attachment..
i've got the answer 1/7 where the series is convergent..
can someone confirm my answer..?

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Dec 9, 2009

Mark44

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Yes, the ratio test gives a ratio of 1/7, so the series converges.

Dec 9, 2009

naspek

Thanks Mark44! =)

1. What is the Series Ratio Test?

The Series Ratio Test is a method used to determine the convergence or divergence of a series. It involves taking the limit of the ratio of consecutive terms in a series and using that limit to determine the behavior of the series.

2. How do I use the Series Ratio Test?

To use the Series Ratio Test, you must first take the limit of the ratio of consecutive terms in the series. If this limit is less than 1, the series is absolutely convergent. If the limit is greater than 1, the series is divergent. If the limit is equal to 1 or the limit does not exist, the test is inconclusive and other methods must be used.

3. What does a ratio of 1/7 mean in the Series Ratio Test?

A ratio of 1/7 in the Series Ratio Test means that the limit of the ratio of consecutive terms in the series is equal to 1/7. This could indicate that the series is convergent, but it is inconclusive and further analysis is needed to determine the convergence or divergence of the series.

4. How accurate is the Series Ratio Test?

The Series Ratio Test is a highly accurate method for determining the convergence or divergence of a series. However, it is not foolproof and can sometimes give inconclusive results. It is important to use other methods and techniques to confirm the results obtained from the Series Ratio Test.

5. Can the Series Ratio Test be used on any series?

The Series Ratio Test can only be used on series that meet certain criteria, such as having positive terms and being monotonically decreasing. If a series does not meet these criteria, the test cannot be applied and other methods must be used.