Which of the following intervals is impossible for the convergence of the power series the summation from n equals 0 to infinity of a sub n times the nth power of x minus 3 ?

Question

Which of the following intervals is impossible for the convergence of the power series  ?

A	0 < x < 6
B	1 ≤ x ≤ 5
C	2 ≤ x ≤ 5
D	2 ≤ x ≤ 4

Answer 1

The given power series involves powers of x - 3. So, the power series converges at the center, x = 3 and the interval of convergence must be centered at 3. Since the interval [2,5] is not centered at 3, the interval [2,5] can't be the interval of convergence.