Question

Calc 2 question on Absolute Convergence. (Just want to make sure I am understanding it properly.)

Answer 1

Okay, so if the Ratio Test or Root Test yields some L < 1 the series converges absolutely. If either of those tests yield some L > 1 the series diverges. And if L = 1 those tests tell you nothing about the convergence/divergence of the series correct?

A series can also be considered absolutely convergent if the Comparison Test, Limit Comparison Test, or Integral Test of the absolute value of the series yields convergence correct?

And finally, if any test for absolute convergence is inconclusive, the series can still be found to be conditionally convergent. Am I correct in assuming that this conditional convergence would be found using the Alternating Series Test?

Anything that I said here wrong, or that I left out? I have a quiz over this tomorrow and I'm not really sure if I'm understanding it correctly.

Answer 2

if the Ratio Test or Root Test yields some L < 1 the series converges absolutely. If either of those tests yield some L > 1 the series diverges. And if L = 1 those tests tell you nothing about the convergence/divergence of the series correct?
where did u get this?

Answer 3

My calc book and professor. (L is referring to the limit, perhaps I should have been more specific about that)\[\lim_{n \rightarrow \infty}\frac{a_{n+1}}{a_n} = L\] like that basically.

Answer 4

hmmm
try to look for another statement for convergence and divergence
rest is good

Answer 5

Another statement for convergence and divergence?