MHB Convergence Condition for Applying Ratio Test to Power Series

[alexmahone]

Given a power series, what is the condition on its coefficients that means the ratio test can be applied?

 

[Dustinsfl]

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.

 

[Prove It]

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).