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Unformatted text preview: not converge absolutely, but does converge on its own, a conditionally convergent series.
Ex: We have seen that the following series converges by the alternating series test. 1 (1) n
n If we take the absolute values (ie change all to positive), we get: 1
| (1) | n n 1 n
n Here the p‐test kicks in (p=1≤1) which means this series diverges.
This means that the original series is not absolutely divergent, but is conditionally convergent (it diverges under absolute, but converges standing on its own). Any series that is not absolutely convergent or conditionally convergent, we simply call this series a divergent series. Strategy for Finding Absolute/Conditional
Step 1: Take the abs...
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- Summer '00
- Calculus, SmartPen Lectures, Lecture Notes, MATH1004, Kyle Harvey