- #1
ColtonCM
- 33
- 2
Homework Statement
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This is the question I have (from a worksheet that is a practice for a quiz). Its a conceptual question (I guess). I understand how to solve ratio test problems.
"Is this test only sufficient, or is it an exact criterion for convergence?"
Homework Equations
Recall the ratio-test: If {an}n∈N is a positive sequence and there is a number a < 1 such that eventually an+1 ≤ a then the series is convergent. If, eventually, an+1 ≥ 1 then the series is divergent.
The Attempt at a Solution
I would assume that it would be considered "only sufficient," since if the result yields a ratio of one, convergence cannot be determined, thus it is not an absolute criterion.
Would this line of reasoning be correct?
Thanks,
Colton