Find a Formula for the Nth Partial Sum of the Series

question 346

Multiple Choice

Find a formula for the nth partial sum of the series and use it to find the series' sum if the series converges.
- $9 - 36 + 144 - 576 + \ldots + ( - 1 ) ^ { n - 1 } 9 \cdot 4 ^ { n - 1 } + \ldots$

• A) \(\frac { 9 \left( 1 - ( - 4 ) ^ { n } \right) } { 4 - 1 }\); series diverges
• B) \(\frac { 9 \left( 1 - ( - 4 ) ^ { n } \right) } { 1 + 4 }\); series diverges
• C) \(\frac { 9 \left( 1 - ( - 4 ) ^ { n } \right) } { 1 + 4 } ; \frac { 9 } { 5 }\)
• D) \(\frac { 9 \left( 1 - ( - 4 ) ^ { n } \right) } { 1 - 4 } ; 3\)