Find the sum, if it exists, of the terms of the infinite geometric sequence.
-$\sum_{i=1}^{\infty} \frac{4}{3}\left(\frac{1}{3}\right)^{i-1}$

A) $\frac{4}{3}$

B) $\frac{1}{2}$

C) 2

D) Does not exist

Question

Find the sum, if it exists, of the terms of the infinite geometric sequence.
-$\sum_{i=1}^{\infty} \frac{4}{3}\left(\frac{1}{3}\right)^{i-1}$

A) $\frac{4}{3}$

B) $\frac{1}{2}$

C) 2

D) Does not exist

Quizplus · Accepted Answer

The series is an infinite geometric series with the first term $a = \frac{4}{3}$ and common ratio $r = \frac{1}{3}$. Since $|r| < 1$, the sum exists and is given by $S = \frac{a}{1-r} = \frac{\frac{4}{3}}{1-\frac{1}{3}} = \frac{\frac{4}{3}}{\frac{2}{3}} = 2$.

Find the Sum, If It Exists, of the Terms of the Infinite