APFIVE Properties of Series Convergence Tests
The table below summarizes properties of several convergence tests for infinite series. All of the following statements regarding these tests are true EXCEPT:
| Test | Conclusion |
|---|---|
| Ratio Test | Inconclusive if L = 1 |
| Integral Test | Requires f(x) to be decreasing |
| nth Term Test | Necessary for convergence |
| Alternating Series | Error bounded by next term |
A
Various convergence tests, such as the Ratio Test and the Integral Test, help determine the behavior of series.
B
If a series passes multiple convergence tests, it is guaranteed to diverge.
C
Some tests, like the Ratio Test, can be inconclusive under certain conditions.
D
The nth term test is a fundamental test that checks the necessary condition for convergence by examining the limit of the sequence’s terms.
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