Let R be the radius of convergence of a power series Σ a n x n . Mark each statement True or False. Justify each answer. (a) The series converges absolutely whenever | x | ≤ R and diverges whenever |...

Let R be the radius of convergence of a power series Σ a_nxⁿ. Mark each statement True or False. Justify each answer.

(a) The series converges absolutely whenever | x | ≤ R and diverges whenever | x | > R.

(b) If R = + ∞, then the series converges absolutely for all real x.

(c) If R = 0, then the series diverges for all real x.