Find the Interval of Convergence of the Power Series $$\sum _ { n = 0 } ^ { \infty } \frac { ( - 1 ) ^ { n } n ! ( x - 10 ) ^ { n } } { ( 9 ) ^ { n } }$$

question 35

Multiple Choice

Find the interval of convergence of the power series. (Be sure to include a check for convergence at the endpoints of the interval.) $$\sum _ { n = 0 } ^ { \infty } \frac { ( - 1 ) ^ { n } n ! ( x - 10 ) ^ { n } } { ( 9 ) ^ { n } }$$

• A) \(\{ 10 \}\)
• B) \(( - 10,10 )\)
• C) \(\{ 0 \}\)
• D) \([ - 10,10 )\)
• E) \(( - \infty , \infty )\)

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