Find the Sum of the Geometric Series for Those X $$\sum _ { n = 0 } ^ { \infty } \frac { ( - 1 ) ^ { n } } { 7 } \frac { 1 } { ( 3 + \sin x ) ^ { n } }$$

question 22

Multiple Choice

Find the sum of the geometric series for those x for which the series converges.
- $$\sum _ { n = 0 } ^ { \infty } \frac { ( - 1 ) ^ { n } } { 7 } \frac { 1 } { ( 3 + \sin x ) ^ { n } }$$

• A) \(\frac { 3 + \sin x } { 7 ( 4 - \sin x ) }\)
• B) \(\frac { 3 + \sin x } { 7 ( 4 + \sin x ) }\)
• C) \(\frac { 7 + \sin x } { 3 ( 4 - \sin x ) }\)
• D) \(\frac { 7 + \sin x } { 3 ( 4 + \sin x ) }\)

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