Provide an Appropriate Response $\sum _ { \mathrm { n } = 0 } ^ { \infty } ( - 1 ) ^ { \mathrm { n } } ( \mathrm { x } - 5 ) ^ { \mathrm { n } }$

question 242

Multiple Choice

Provide an appropriate response.
-If the series $\sum _ { \mathrm { n } = 0 } ^ { \infty } ( - 1 ) ^ { \mathrm { n } } ( \mathrm { x } - 5 ) ^ { \mathrm { n } }$ is integrated twice term by term, for what value(s) of $\mathrm { x }$ (if any) does the new series converge and for which the given series does not converge?

• A) x = 4, x = 6
• B) x = 4
• C) none
• D) x = 6

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