ap-calculus-bc 2012 Q22

ap-calculus-bc · Usa · practice-exam Sequences and Series Power Series Expansion and Radius of Convergence
The power series $\sum _ { n = 0 } ^ { \infty } a _ { n } ( x - 3 ) ^ { n }$ converges at $x = 5$. Which of the following must be true?
(A) The series diverges at $x = 0$.
(B) The series diverges at $x = 1$.
(C) The series converges at $x = 1$.
(D) The series converges at $x = 2$.
(E) The series converges at $x = 6$.
The power series $\sum _ { n = 0 } ^ { \infty } a _ { n } ( x - 3 ) ^ { n }$ converges at $x = 5$. Which of the following must be true?

(A) The series diverges at $x = 0$.

(B) The series diverges at $x = 1$.

(C) The series converges at $x = 1$.

(D) The series converges at $x = 2$.

(E) The series converges at $x = 6$.