Find the Values of X for Which the Series $\sum _ { n = 1 } ^ { \infty } \left( 2 x + \frac { 1 } { 2 } \right) ^ { n }$

question 36

Multiple Choice

Find the values of x for which the series $\sum _ { n = 1 } ^ { \infty } \left( 2 x + \frac { 1 } { 2 } \right) ^ { n }$ converges.

• A) \(\left( - \frac { 3 } { 2 } , \frac { 1 } { 2 } \right)\)
• B) \(\left( - \frac { 3 } { 2 } , \frac { 1 } { 2 } \right]\)
• C) \(\left( - \frac { 1 } { 2 } , \frac { 1 } { 2 } \right)\)
• D)0
• E) \(\left[ - \frac { 3 } { 4 } , \frac { 1 } { 4 } \right)\)
• F) \(\left[ - \frac { 3 } { 2 } , \frac { 1 } { 2 } \right]\)
• G) \(\left( - \frac { 3 } { 4 } , \frac { 1 } { 4 } \right)\)
• H) \(( - \infty , \infty )\)

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