Find the sum of the geometric series, if possible.
-$$\sum _ { n = 1 } ^ { \infty } \left( \frac { 3 } { 4 } \right) ^ { n - 1 }$$
A) Sum does not exist
B) $\frac { 1 } { 4 }$
C) 4
D) 3

Question

Quizplus · Accepted Answer

The given series is a geometric series with the first term $a = \left(\frac{3}{4}\right)^{1-1} = 1$ and common ratio $r = \frac{3}{4}$. The sum of an infinite geometric series is given by $S = \frac{a}{1 - r}$, provided $|r| < 1$. Substituting the given values, we get $S = \frac{1}{1 - \frac{3}{4}} = \frac{1}{\frac{1}{4}} = 4$.

Find the Sum of the Geometric Series, If Possible ∑n=1∞(34)n−1\sum _ { n = 1 } ^ { \infty } \left( \frac { 3 } { 4 } \right) ^ { n - 1 }n=1∑∞​(43​)n−1

Find the Sum of the Geometric Series, If Possible $\sum _ { n = 1 } ^ { \infty } \left( \frac { 3 } { 4 } \right) ^ { n - 1 }$