D'Alembert Ratio Test: Convergence test

[ruby_duby]

Hi this is just a general question about using the ratio test for convergence.

If I have to carry out the test to find out if something converges (and I don't need to find out if its absolutely converges, but just convergence), then can my answer to the test be negative?

Or does the formula for the ratio test when finding the limit, use the modulus?

 

[HallsofIvy]

Strictly speaking, the ratio test only applies to sequences of positive numbers so, yes, it applies to the modulus (absolute value).