Let R be the radius of convergence of a power series Σa n x n . Mark each statement True or False. Justify each answer. (a) R = limn → ∞ | a n+1 /a n |, provided that this limit exists. (b) If 0 (c)...

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

(a) R = limn → ∞ | a_n+1/a_n
|, provided that this limit exists.

(b) If 0 <><>

(c) If an ≥ 0 for all n, then for any x ∈ R, the series Σa_nxⁿ
either converges absolutely or diverges.