Express the Sum Using Summation Notation $\frac { 4 } { 5 } - \frac { 16 } { 25 } + \frac { 64 } { 125 } - \cdots + ( - 1 ) ^ { ( 11 + 1 ) } \left( \frac { 4 } { 5 } \right) ^ { 11 }$

Multiple Choice

Express the sum using summation notation.
- $\frac { 4 } { 5 } - \frac { 16 } { 25 } + \frac { 64 } { 125 } - \cdots + ( - 1 ) ^ { ( 11 + 1 ) } \left( \frac { 4 } { 5 } \right) ^ { 11 }$

A)
$\sum _ { k = 1 } ^ { 11 } ( - 1 ) ^ { ( k + 1 ) } \left( \frac { 4 } { 5 } \right) ^ { k }$
B)
$\sum _ { k = 1 } ^ { 12 } ( - 1 ) ^ { ( k + 1 ) } \left( \frac { 4 } { 5 } \right) ^ { k }$
C)
$\sum_{k=1}^{11}\left(\frac{4}{5}\right) ^{k}$
D)
$\sum_{k=1}^{n}(-1) ^{(k+1) }\left(\frac{4}{5}\right) ^{k}$