Write the sum using summation notation, assuming the suggested pattern continues.
-$$2 - 4 + 8 - 16 + \ldots$$
A) $\sum _ { n = 0 } ^ { \infty } 2 \cdot 2 ^ { n + 1 }$
B) $\sum _ { n = 0 } ^ { \infty } 2 ( - 2 ) ^ { n + 1 }$
C) $\sum _ { n = 0 } ^ { \infty } 2 \cdot 2 ^ { n }$
D) $\sum _ { n = 0 } ^ { \infty } 2 ( - 2 ) ^ { n }$

Question

Quizplus · Accepted Answer

The pattern alternates between positive and negative terms, which can be represented by $(-2)^n$. The first term is $2 = 2 \cdot (-2)^0$, indicating that the base of the exponent should be $(-2)$ and start with $n=0$. Therefore, the correct representation is $2(-2)^n$.

Write the Sum Using Summation Notation, Assuming the Suggested Pattern 2−4+8−16+…2 - 4 + 8 - 16 + \ldots2−4+8−16+…

Write the Sum Using Summation Notation, Assuming the Suggested Pattern $2 - 4 + 8 - 16 + \ldots$