Find the sum of the infinite geometric series. $\sum _ { n = 1 } ^ { \infty } 3 \left( \frac { 1 } { 2 } \right) ^ { n - 1 }$
A) $6$
B) $3$
C) $12$
D) $9$
E) $18$

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, $a = 3$ and $r = \frac{1}{2}$, so $S = \frac{3}{1 - \frac{1}{2}} = \frac{3}{\frac{1}{2}} = 6$.

Find the Sum of the Infinite Geometric Series ∑n=1∞3(12)n−1\sum _ { n = 1 } ^ { \infty } 3 \left( \frac { 1 } { 2 } \right) ^ { n - 1 }∑n=1∞​3(21​)n−1

Find the Sum of the Infinite Geometric Series $\sum _ { n = 1 } ^ { \infty } 3 \left( \frac { 1 } { 2 } \right) ^ { n - 1 }$