Find the sum of the geometric series, if possible.
-$$\sum _ { n = 1 } ^ { \infty } \left( - \frac { 1 } { 2 } \right) ^ { n }$$
A) $\frac { 2 } { 3 }$
B) $- 1$
C) 2
D) $- \frac { 1 } { 3 }$

Question

Quizplus · Accepted Answer

The sum of an infinite geometric series can be found using the formula $S = \frac{a}{1 - r}$, where $a$ is the first term and $r$ is the common ratio. Here, $a = \left(-\frac{1}{2}\right)^1 = -\frac{1}{2}$ and $r = -\frac{1}{2}$. Plugging these values into the formula gives $S = \frac{-\frac{1}{2}}{1 - (-\frac{1}{2})} = \frac{-\frac{1}{2}}{\frac{3}{2}} = -\frac{1}{3}$.

Find the Sum of the Geometric Series, If Possible ∑n=1∞(−12)n\sum _ { n = 1 } ^ { \infty } \left( - \frac { 1 } { 2 } \right) ^ { n }n=1∑∞​(−21​)n

Find the Sum of the Geometric Series, If Possible $\sum _ { n = 1 } ^ { \infty } \left( - \frac { 1 } { 2 } \right) ^ { n }$