Ratio Test for Finding the 1(circled part) - Understanding the Process

Thread starter foo9008
Start date Mar 6, 2016
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Ratio Ratio test Test

In summary, 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 successive terms and if the limit is less than 1, the series is convergent. It is generally used for series with factorials, exponentials, or powers of n and can also prove absolute convergence. However, it has limitations as it can only be used on series with positive terms and may not be conclusive for certain series. It is considered a powerful test, but other tests may be more efficient for certain series.

Mar 6, 2016

foo9008

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Homework Statement

where does the 1(circled part) come from ? is it a mistake ?

Homework Equations

The Attempt at a Solution

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Mar 6, 2016

Filip Larsen

Gold Member

Try look closer. There is a difference in the second expression apart from the 1.

Related to Ratio Test for Finding the 1(circled part) - Understanding the Process

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 successive terms in the series. If the limit is less than 1, the series is convergent. If the limit is greater than 1 or undefined, the series is divergent.

2. When should the ratio test be used?

The ratio test is generally used for series that involve factorials, exponentials, or powers of n. It is also useful for series with alternating signs or alternating terms.

3. Can the ratio test be used to prove absolute convergence?

Yes, the ratio test can be used to prove absolute convergence. If the limit of the ratio is less than 1, the series is absolutely convergent, meaning that the series of absolute values converges.

4. Are there any limitations to the ratio test?

Yes, the ratio test can only be used on series with positive terms. It also may not be conclusive for certain series, such as alternating series or those with terms that approach 1.

5. How does the ratio test compare to other convergence tests?

The ratio test is considered to be one of the most powerful convergence tests, as it can determine the convergence or divergence of many types of series. However, it may not always be the most efficient method and other tests, such as the comparison test or the integral test, may be more suitable for certain series.