Express the sum using summation notation.
-$$\frac { 4 } { 5 } - \frac { 16 } { 25 } + \frac { 64 } { 125 } - \cdots + ( - 1 ) ^ { ( 13 + 1 ) } \left( \frac { 4 } { 5 } \right) ^ { 13 }$$
A)
$$\sum _ { k = 1 } ^ { n } ( - 1 ) ^ { ( k + 1 ) } \left( \frac { 4 } { 5 } \right) ^ { k }$$
B)
$$\sum _ { \mathrm { k } = 1 } ^ { 14 } ( - 1 ) ^ { ( \mathrm { k } + 1 ) } \left( \frac { 4 } { 5 } \right) ^ { \mathrm { k } }$$
C)
$$\sum _ { k = 1 } ^ { 13 } ( - 1 ) ^ { ( k + 1 ) } \left( \frac { 4 } { 5 } \right) ^ { \mathrm { k } }$$

D)

$\sum _ { k = 1 } ^ { 13 } \left( \frac { 4 } { 5 } \right) ^ { k }$

Question

Express the sum using summation notation.
-$$\frac { 4 } { 5 } - \frac { 16 } { 25 } + \frac { 64 } { 125 } - \cdots + ( - 1 ) ^ { ( 13 + 1 ) } \left( \frac { 4 } { 5 } \right) ^ { 13 }$$
A)
$$\sum _ { k = 1 } ^ { n } ( - 1 ) ^ { ( k + 1 ) } \left( \frac { 4 } { 5 } \right) ^ { k }$$
B)
$$\sum _ { \mathrm { k } = 1 } ^ { 14 } ( - 1 ) ^ { ( \mathrm { k } + 1 ) } \left( \frac { 4 } { 5 } \right) ^ { \mathrm { k } }$$
C)
$$\sum _ { k = 1 } ^ { 13 } ( - 1 ) ^ { ( k + 1 ) } \left( \frac { 4 } { 5 } \right) ^ { \mathrm { k } }$$

D)

$\sum _ { k = 1 } ^ { 13 } \left( \frac { 4 } { 5 } \right) ^ { k }$

Quizplus · Accepted Answer

The series is a geometric series with alternating signs, starting from $ k = 1 $ to $ k = 13 $.

Express the Sum Using Summation Notation 45−1625+64125−⋯+(−1)(13+1)(45)13\frac { 4 } { 5 } - \frac { 16 } { 25 } + \frac { 64 } { 125 } - \cdots + ( - 1 ) ^ { ( 13 + 1 ) } \left( \frac { 4 } { 5 } \right) ^ { 13 }54​−2516​+12564​−⋯+(−1)(13+1)(54​)13

Express the Sum Using Summation Notation $\frac { 4 } { 5 } - \frac { 16 } { 25 } + \frac { 64 } { 125 } - \cdots + ( - 1 ) ^ { ( 13 + 1 ) } \left( \frac { 4 } { 5 } \right) ^ { 13 }$