The power power-series \( \displaystyle \sum_{n=0}^\infty a_n(x-3)^n \) converges at \(x=5\). Which of the following must be true?

The Taylor power-series is centered around \(x=3\). Since it converges at \(x=5\), the radius of convergence must be \(2\).

The power-series converges for \( 1\lt x \lt 5 \). The endpoints would have to be tested seperately, so we do not know if it converges at \(x=1\).