Find the sum of the infinite series. $\sum _ { i = 1 } ^ { \infty } 3 \left( - \frac { 1 } { 4 } \right) ^ { i }$
A)undefined
B)3
C) $- \frac { 3 } { 5 }$
D) $\frac { 6 } { 5 }$
E) $- \frac { 1 } { 1 }$

Question

Find the sum of the infinite series. $\sum _ { i = 1 } ^ { \infty } 3 \left( - \frac { 1 } { 4 } \right) ^ { i }$
A)undefined
B)3
C) $- \frac { 3 } { 5 }$  
D) $\frac { 6 } { 5 }$
E) $- \frac { 1 } { 1 }$

Quizplus · Accepted Answer

This 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 $S = \frac{a}{1 - r}$, where $|r| < 1$. Plugging in the values, 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 Infinite Series ∑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 Infinite Series $\sum _ { i = 1 } ^ { \infty } 3 \left( - \frac { 1 } { 4 } \right) ^ { i }$