Determine whether the infinite geometric series converges or diverges. If it converges, find its sum.
-$$4 - 1 + \frac { 1 } { 4 } - \cdots$$
A) Converges; - 1
B) Converges; 4
C) Converges; $\frac { 16 } { 5 }$
D) Converges; 3

Question

Quizplus · Accepted Answer

The series is a geometric series with the first term $a = 4$ 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, $S = \frac{4}{1 - (-\frac{1}{4})} = \frac{4}{\frac{5}{4}} = \frac{16}{5}$, so the series converges to $\frac{16}{5}$.

Determine Whether the Infinite Geometric Series Converges or Diverges 4−1+14−⋯4 - 1 + \frac { 1 } { 4 } - \cdots4−1+41​−⋯

Determine Whether the Infinite Geometric Series Converges or Diverges $4 - 1 + \frac { 1 } { 4 } - \cdots$