Use the Formula for the Sum of an Infinite Geometric Series
-$$2 - \frac { 1 } { 2 } + \frac { 1 } { 8 } - \frac { 1 } { 32 } + \ldots$$
A) $\frac { 8 } { 5 }$
B) $\frac { 3 } { 2 }$
C) $- \frac { 1 } { 2 }$
D) does not exist

Question

Quizplus · Accepted Answer

The given series is an infinite geometric series with the first term $a = 2$ and common ratio $r = -\frac{1}{4}$. The sum of an infinite geometric series is given by $S = \frac{a}{1 - r}$, where $|r| < 1$. Substituting $a = 2$ and $r = -\frac{1}{4}$ into the formula gives $S = \frac{2}{1 - (-\frac{1}{4})} = \frac{2}{\frac{5}{4}} = \frac{8}{5}$.

Use the Formula for the Sum of an Infinite Geometric 2−12+18−132+…2 - \frac { 1 } { 2 } + \frac { 1 } { 8 } - \frac { 1 } { 32 } + \ldots2−21​+81​−321​+…

Use the Formula for the Sum of an Infinite Geometric $2 - \frac { 1 } { 2 } + \frac { 1 } { 8 } - \frac { 1 } { 32 } + \ldots$