MATH 01131 · Sequences & series

Radius/interval of convergence

Definition

For Σ cₙ(x−a)ⁿ, radius R is such that the series converges for |x−a|<R and diverges for |x−a|>R. Endpoints x=a±R must be tested separately.

Find R via ratio/root test: L=lim |cₙ₊₁/cₙ| then R=1/L (patterns vary).

Always check endpoints with other tests after finding R.

Interval might be open, closed, or half-open.

Flip through these until you can say the answer before revealing it.

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