Power series: Σₙ₌₀ aₙ(x−c)ⁿ. Radius of convergence R = 1/lim sup|aₙ|^(1/n) = lim|aₙ/aₙ₊₁|. Converges absolutely for |x−c| < R, diverges for |x−c| > R. Check endpoints separately. Common: eˣ (R=∞), 1/(1−x) (R=1), ln(1+x) (R=1).
How to Use
Select a function:
- f(x): Preset function
- Series: Power series
- R: Radius of convergence
Convergence
|x−c| < R: absolutely convergent. |x−c| > R: divergent. |x−c| = R: must check each endpoint individually (could converge or diverge). Uniform convergence on compact subsets of (-R,R).
Operations
- Add/subtract term by term
- Differentiate: Σnaₙxⁿ⁻¹ (same R)
- Integrate: Σaₙxⁿ⁺¹/(n+1) (same R)
- Multiply: Cauchy product
Step-by-Step Instructions
- 1Select function.
- 2View series.
- 3Get radius R.
- 4Check interval.
- 5Evaluate partial sum.