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

question 311

Multiple Choice

Provide an appropriate response.
-If the series $\sum _ { \mathrm { n } = 0 } ^ { \infty } ( - 1 ) ^ { \mathrm { n } } ( \mathrm { x } + 1 ) ^ { \mathrm { n } }$ is integrated twice term by term, for what value(s) of $\mathrm { x }$ does the new series converge?

• A) \(- 2 \leq x < 0\)
• B) \(- 2 \leq x \leq 0\)
• C) \(- 2 < x < 0\)
• D) \(- 2 < x \leq 0\)

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