Find the indicated partial sum of the series. $$\sum _ { i = 1 } ^ { \infty } 4 \left( - \frac { 1 } { 2 } \right) ^ { i }$$ fourth partial sum
A) $\frac { 3 } { 4 }$
B) $- \frac { 17 } { 12 }$
C) $\frac { 11 } { 4 }$
D) $\frac { 1 } { 4 }$
E) $- \frac { 5 } { 4 }$

Question

Find the indicated partial sum of the series. $$\sum _ { i = 1 } ^ { \infty } 4 \left( - \frac { 1 } { 2 } \right) ^ { i }$$ fourth partial sum
A) $\frac { 3 } { 4 }$
B) $- \frac { 17 } { 12 }$ ​
C) $\frac { 11 } { 4 }$ ​
D) $\frac { 1 } { 4 }$ ​
E) $- \frac { 5 } { 4 }$ ​

Quizplus · Accepted Answer

The series is geometric with first term $a = -2$ and common ratio $r = -\frac{1}{2}$. The fourth partial sum is $S_4 = a \frac{1-r^4}{1-r} = -2 \frac{1-(-\frac{1}{2})^4}{1+\frac{1}{2}} = -\frac{5}{4}$.

Find the Indicated Partial Sum of the Series ∑i=1∞4(−12)i\sum _ { i = 1 } ^ { \infty } 4 \left( - \frac { 1 } { 2 } \right) ^ { i }i=1∑∞​4(−21​)i

Find the Indicated Partial Sum of the Series $\sum _ { i = 1 } ^ { \infty } 4 \left( - \frac { 1 } { 2 } \right) ^ { i }$