Find the Sum of the Geometric Series for Those X $$\sum _ { \mathrm { n } = 0 } ^ { \infty } ( - 1 ) ^ { \mathrm { n } } \left( \frac { \mathrm { x } - 5 } { 2 } \right) ^ { \mathrm { n } }$$

question 442

Multiple Choice

Find the sum of the geometric series for those x for which the series converges.
- $$\sum _ { \mathrm { n } = 0 } ^ { \infty } ( - 1 ) ^ { \mathrm { n } } \left( \frac { \mathrm { x } - 5 } { 2 } \right) ^ { \mathrm { n } }$$

• A) \(\frac { 2 } { 3 - x }\)
• B) \(\frac { 2 } { - 3 - x }\)
• C) \(\frac { 2 } { 3 + x }\)
• D) \(\frac { 2 } { - 3 + x }\)

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