Write the given series in summation notation. $2 - 4 + 8 - 16 + 32 - 64 + 128$
A) $\sum _ { i = 1 } ^ { 7 } 4 ^ { i } ( - 1 ) ^ { i }$
B) $\sum _ { i = 1 } ^ { 7 } 4 ^ { i } ( - 1 ) ^ { i + 1 }$
C) $\sum _ { i = 1 } ^ { 7 } 2 ^ { i } ( - 1 ) ^ { i + 1 }$
D) $\sum _ { i = 1 } ^ { 7 } 2 ^ { i } ( - 1 ) ^ { i }$
E) $\sum _ { i = 1 } ^ { 7 } 3 ^ { i } ( - 1 ) ^ { i }$

Question

Quizplus · Accepted Answer

The series alternates signs and doubles each term, starting with 2. This is represented by $2^i$ for the doubling effect. The alternating signs are represented by $(-1)^{i+1}$, ensuring the series starts with a positive term.

Write the Given Series in Summation Notation 2−4+8−16+32−64+1282 - 4 + 8 - 16 + 32 - 64 + 1282−4+8−16+32−64+128

Write the Given Series in Summation Notation $2 - 4 + 8 - 16 + 32 - 64 + 128$