Find the sum of the sequence.
-$$\sum _ { k = 1 } ^ { 4 } ( - 1 ) ^ { k \cdot - 8 k }$$
A) -16
B) -80
C) 80
D) 4,096

Question

Quizplus · Accepted Answer

Explanation:The sum of the sequence is:$$\sum _ { k = 1 } ^ { 4 } ( - 1 ) ^ { k \cdot - 8 k } = ( - 1 ) ^ { 1 \cdot - 8 \cdot 1 } + ( - 1 ) ^ { 2 \cdot - 8 \cdot 2 } + ( - 1 ) ^ { 3 \cdot - 8 \cdot 3 } + ( - 1 ) ^ { 4 \cdot - 8 \cdot 4 }$$$$= ( - 1 ) ^ { - 8 } + ( - 1 ) ^ { - 16 } + ( - 1 ) ^ { - 24 } + ( - 1 ) ^ { - 32 }$$$$= 1 + 1 + 1 + 1 = 4$$$$= 4 \cdot - 4 = - 16$$

Find the Sum of the Sequence ∑k=14(−1)k⋅−8k\sum _ { k = 1 } ^ { 4 } ( - 1 ) ^ { k \cdot - 8 k }k=1∑4​(−1)k⋅−8k

Find the Sum of the Sequence $\sum _ { k = 1 } ^ { 4 } ( - 1 ) ^ { k \cdot - 8 k }$