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

Question

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

	0 < x < 6
	1 ≤ x ≤ 5
	2 ≤ x ≤ 5
	2 ≤ x ≤ 4

Answer 1

The terms of the given series involve powers of x-3. So, the series is centered at x = 3 and converges there. The interval of convergence must be centered at 3. Since the interval [2,5] is not centered at 3, [2,5] can not be the interval of convergence.