MHB Convergence Condition for Applying Ratio Test to Power Series

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The discussion centers on the conditions under which the ratio test can be applied to power series. It is suggested that the ratio test can always be used, although other tests may be more convenient for specific series. A key point is that the ratio test should be applied to the series of absolute values to demonstrate absolute convergence. This approach ensures that the series is bounded above and below by the series of absolute values. Understanding these conditions is essential for correctly applying the ratio test to power series.
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Given a power series, what is the condition on its coefficients that means the ratio test can be applied?
 
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Alexmahone said:
Given a power series, what is the condition on its coefficients that means the ratio test can be applied?

I think it can always be applied. Other test just may be easier for a given power series.
 
Alexmahone said:
Given a power series, what is the condition on its coefficients that means the ratio test can be applied?

You actually should always do the ratio test on the series of ABSOLUTE VALUES, to prove absolute convergence (i.e. to show the series is bounded both above and below by the series of absolute values and the negative of the series of absolute values).
 

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