Calculus › Section J · Infinite series › Topic J.9
Representing functions as power series
One geometric series, plus the rules of calculus, manufactures power series for logarithms, arctangents and functions no antiderivative can touch. The trick is that inside its radius, a power series behaves exactly like a polynomial.
In this topic
- One known representation, many targets
- Substitution: bending the master series
- Term-by-term calculus
- Worked example: the series for ln(1 + x)
- Worked example: the series for arctan x
- Worked example: differentiating instead
- Applied: computing a logarithm by hand
- Common mistakes to avoid
- Key takeaways
This topic is part of Wuanberri Pro. Checking your access…
Standards: 10 (BC)