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) $\frac { 9 \left( 1 - ( - 4 ) ^ { n } \right) } { 1 - 4 } ; 3$

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The Answer of 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) $\frac { 9 \left( 1 - ( - 4 ) ^ { n } \right) } { 1 - 4 } ; 3$

Find a Formula for the Nth Partial Sum of the Series