The Power Series $\sum _ { n = 1 } ^ { \infty } a _ { n } ( x - 2 ) ^ { n }$

question 88

Essay

The power series $\sum _ { n = 1 } ^ { \infty } a _ { n } ( x - 2 ) ^ { n }$ and $\sum _ { n = 1 } ^ { \infty } b _ { n } ( x - 3 ) ^ { n }$ both converge at $x = 6$ . Find the largest interval over which both series must converge.