Find the sum of the series, if possible.
-$$\sum _ { i = 1 } ^ { \infty } 3 \left( - \frac { 1 } { 4 } \right) ^ { i }$$
A) $- 1$
B) $- \frac { 3 } { 5 }$
C) Not possible
D) $\frac { 3 } { 5 }$

Question

Quizplus · Accepted Answer

This series is a geometric series with the first term $a = 3(-\frac{1}{4})$ and common ratio $r = -\frac{1}{4}$. The sum of an infinite geometric series is given by $S = \frac{a}{1 - r}$, provided $|r| < 1$. Substituting $a = 3(-\frac{1}{4})$ and $r = -\frac{1}{4}$, we get $S = \frac{3(-\frac{1}{4})}{1 - (-\frac{1}{4})} = \frac{-\frac{3}{4}}{\frac{5}{4}} = -\frac{3}{5}$.

Find the Sum of the Series, If Possible ∑i=1∞3(−14)i\sum _ { i = 1 } ^ { \infty } 3 \left( - \frac { 1 } { 4 } \right) ^ { i }i=1∑∞​3(−41​)i

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