Limit Comp Test for Polynomial w/Neg Coeff: Use Abs Vals

Thread starter 2slowtogofast
Start date Nov 15, 2009
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Improper integral Integral

In summary, a limit comp test for polynomial with negative coefficients is a method used to determine the convergence or divergence of a polynomial series with negative coefficients. It involves taking the absolute values of the coefficients and comparing the resulting series with a known convergent or divergent series. To perform the test, the absolute values of the coefficients are compared with a known convergent or divergent series, such as the geometric series or the p-series. The use of absolute values is important because it allows us to focus on the magnitude of the coefficients rather than their signs. However, this method has limitations and can only be used for polynomial series with negative coefficients that alternate in sign and have a non-zero limit as n approaches infinity. It cannot be used for polynomial

Nov 15, 2009

2slowtogofast

if you use the limit comp test to show a polynomial behaves like it's highest powered term and that term has a negitive coefficient can the test still be used but with abs vals

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Nov 15, 2009

n!kofeyn

Could you clarify what you are asking and the context of the problem?

Related to Limit Comp Test for Polynomial w/Neg Coeff: Use Abs Vals

1. What is a limit comp test for polynomial with negative coefficients?

A limit comp test for polynomial with negative coefficients is a method used to determine the convergence or divergence of a polynomial series with negative coefficients. It involves taking the absolute values of the coefficients and comparing the resulting series with a known convergent or divergent series.

2. How is a limit comp test performed for polynomial with negative coefficients?

To perform a limit comp test for polynomial with negative coefficients, you first need to take the absolute values of all the coefficients in the polynomial series. Then, you compare the resulting series with a known convergent or divergent series, such as the geometric series or the p-series. If the resulting series is smaller than the known convergent series, the polynomial series is convergent. If it is larger, the polynomial series is divergent.

3. What is the purpose of using absolute values in a limit comp test for polynomial with negative coefficients?

The use of absolute values in a limit comp test for polynomial with negative coefficients allows us to ignore the signs of the coefficients and focus on their magnitude. This is important because negative coefficients can cause the polynomial series to alternate between positive and negative terms, making it difficult to determine convergence or divergence based on the original series.

4. Are there any limitations to using a limit comp test for polynomial with negative coefficients?

Yes, there are some limitations to using a limit comp test for polynomial with negative coefficients. This method only works for polynomial series with negative coefficients that alternate in sign. If the polynomial series has negative coefficients that do not alternate, then the test may not accurately determine convergence or divergence.

5. Can a limit comp test for polynomial with negative coefficients be used for all types of polynomial series?

No, a limit comp test for polynomial with negative coefficients is only applicable to polynomial series with negative coefficients. It cannot be used for polynomial series with positive coefficients or non-polynomial series. Additionally, the series must have a non-zero limit as n approaches infinity in order for the test to be effective.