Calculus › Section J · Infinite series › Topic J.5
Alternating series
The harmonic series diverges, yet flip every second sign and it converges. Alternating series show that cancellation is a genuine source of convergence, and they come with the best error estimate in the subject.
In this topic
- Cancellation changes everything
- The alternating series test
- Why it works: a narrowing corridor
- Worked example: the alternating harmonic series
- The alternating series error bound
- Absolute versus conditional convergence
- Why the distinction matters: rearrangements
- Worked example: classifying by kind of convergence
- Common mistakes to avoid
- Key takeaways
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Standards: 10 (BC)