Determine if the infinite geometric series converges or diverges. If the series converges, find its sum.
-$$3 - \frac { 3 } { 4 } + \frac { 3 } { 16 } - \cdots$$
A) diverges
B) converges, 3
C) converges, $\frac { 12 } { 5 }$
D) converges, $- \frac { 3 } { 4 }$

Question

Quizplus · Accepted Answer

The series is a geometric series with the first term $a = 3$ and common ratio $r = -\frac{1}{4}$. The sum of an infinite geometric series is given by $S = \frac{a}{1 - r}$ if $|r| < 1$. Here, $S = \frac{3}{1 - (-\frac{1}{4})} = \frac{3}{\frac{5}{4}} = \frac{3 \times 4}{5} = \frac{12}{5}$, so the series converges to $\frac{12}{5}$.

Determine If the Infinite Geometric Series Converges or Diverges 3−34+316−⋯3 - \frac { 3 } { 4 } + \frac { 3 } { 16 } - \cdots3−43​+163​−⋯

Determine If the Infinite Geometric Series Converges or Diverges $3 - \frac { 3 } { 4 } + \frac { 3 } { 16 } - \cdots$