Calculus › Section J · Infinite series › Topic J.8
Power series
A power series is an infinite polynomial: fix a centre, stack up powers of (x - a), and let the series define a brand-new function. Where it converges is governed by one number, the radius, plus two delicate endpoint checks.
In this topic
- A polynomial that never ends
- The shape of the convergence region
- Why the tests see only distance
- Worked example: radius and both endpoints
- Worked example: both extremes
- Absolute inside, wild at the edges
- Convergence region versus the function
- Common mistakes to avoid
- Key takeaways
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Standards: 10 (BC)