Which statement best describes the convergence behavior of a power series n=0∑∞an(x−c)n relative to its radius of convergence R?
a) The series converges absolutely for ∣x−c∣<R and ∣x−c∣=R, and diverges for ∣x−c∣>R.
b) The series converges conditionally for ∣x−c∣<R, but diverges for ∣x−c∣≥R.
c) The series converges absolutely for ∣x−c∣<R, may converge conditionally or diverge at ∣x−c∣=R, and diverges for ∣x−c∣>R.
d) The series converges absolutely for ∣x−c∣<R, diverges at ∣x−c∣=R, and may converge or diverge for ∣x−c∣>R.