Determine whether the infinite geometric series converges or diverges. If it converges, find its sum.
-$$1 + \frac { 1 } { 2 } + \frac { 1 } { 4 } + \cdots$$
A) Converges; 2
B) Converges; 1
C) Converges; $\frac { 3 } { 2 }$
D) Converges; $\frac { 1 } { 2 }$

Question

Quizplus · Accepted Answer

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

Determine Whether the Infinite Geometric Series Converges or Diverges 1+12+14+⋯1 + \frac { 1 } { 2 } + \frac { 1 } { 4 } + \cdots1+21​+41​+⋯

Determine Whether the Infinite Geometric Series Converges or Diverges $1 + \frac { 1 } { 2 } + \frac { 1 } { 4 } + \cdots$