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.

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The Answer of 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.

The Power Series ∑n=1∞an(x−2)n\sum _ { n = 1 } ^ { \infty } a _ { n } ( x - 2 ) ^ { n }∑n=1∞​an​(x−2)n

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