A power series centered at converges at but diverges at
MATHEMATICS · Single correct · AP · Calculus BC · Infinite Sequences and Series · Infinite Sequences and Series
Problem
A power series centered at x=3 converges at x=4 but diverges at x=2. After integrating the series term by term, which of the following statements best describes the interval of convergence of the antiderivative?
(a) The radius remains 1, and convergence behaviour at both endpoints is unchanged.
(b) The radius remains 1, and convergence at each endpoint must be tested separately because it may change at x=2 and x=4.
(c) The radius remains 1, and after integration the series converges at both x=2 and x=4.
(d) The radius increases to 2, and the series converges at the same endpoints as before.