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)
$\sum_{k=1}^{n}(-1)^{(k+1)}\left(\frac{4}{5}\right)^{k}$

Question

Quizplus · Accepted Answer

The sum is a geometric series with first term $\frac { 4 } { 5 }$, common ratio $\frac { 4 } { 5 }$, and 11 terms.

Express the Sum Using Summation Notation 45−1625+64125−⋯+(−1)(11+1)(45)11\frac { 4 } { 5 } - \frac { 16 } { 25 } + \frac { 64 } { 125 } - \cdots + ( - 1 ) ^ { ( 11 + 1 ) } \left( \frac { 4 } { 5 } \right) ^ { 11 }54​−2516​+12564​−⋯+(−1)(11+1)(54​)11

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