For a power series Σ a_n (x−c)^n, there exists R ∈ [0,∞] (Cauchy–Hadamard: 1/R = limsup |a_n|^{1/n}) such that the series converges absolutely for |x−c|<R and diverges for |x−c|>R.
For a power series Σ a_n (x−c)^n, there exists R ∈ [0,∞] (Cauchy–Hadamard: 1/R = limsup |a_n|^{1/n}) such that the series converges absolutely for |x−c|<R and diverges for |x−c|>R.