Find the partial sum of the given sequence.
-$\mathrm { S } _ { \infty }$ of the sequence $4 , - \frac { 4 } { 3 } , \frac { 4 } { 9 } , \cdots$
A) 4
B) 3
C) $- \frac { 4 } { 3 }$
D) $\frac { 8 } { 3 }$

Question

Quizplus · Accepted Answer

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

Find the Partial Sum of the Given Sequence S∞\mathrm { S } _ { \infty }S∞​

Find the Partial Sum of the Given Sequence $\mathrm { S } _ { \infty }$