Use the geometric series formula to find the sum of 1

Question

Use the geometric series formula to find the sum of 1 - q + q² - q³ + q⁴. A) $\frac { (-q) ^ { 5 } - 1 } { (-q) - 1 }$ B) $\frac { q ^ { 5 } - 1 } { q - 1 }$ C) $\frac { (-q) ^ { 4 } - 1 } { (-q) - 1 }$ D) $\frac { q ^ { 4 } - 1 } { q - 1 }$

Quizplus · Accepted Answer

The series is a geometric series with the first term $a = 1$ and common ratio $r = -q$. The sum of the first $n$ terms of a geometric series is given by $S_n = \frac{a(r^n - 1)}{r - 1}$. Here, $n = 5$, so the sum is $\frac{1((-q)^5 - 1)}{-q - 1}$.