- #1
twisted079
- 25
- 1
I have a question about the ratio test. Suppose it proves inconclusive, we must than use another test to check for conditional convergence - 1) this test has to be associated with an alternating series, such as the Alternating Series Test, correct? (we wouldn't be able to use something like Integral Test, right?)
2) I noticed in the examples we use Alternating Series Test, if this test proves conditionally convergent, I know it doesn't prove Absolute Convergence. So now we would have to check for Absolute Convergence, correct? *** In this case, we can use tests such as the Comparison Test, which neglects that it is an alternating series? So basically at this point we take the absolute value of the series, which neglects any negatives, leaving it open for other tests?
2) I noticed in the examples we use Alternating Series Test, if this test proves conditionally convergent, I know it doesn't prove Absolute Convergence. So now we would have to check for Absolute Convergence, correct? *** In this case, we can use tests such as the Comparison Test, which neglects that it is an alternating series? So basically at this point we take the absolute value of the series, which neglects any negatives, leaving it open for other tests?