Find the sum of the geometric series. $$5 + 1 + \frac { 1 } { 5 } + \frac { 1 } { 25 } + \frac { 1 } { 125 }$$

Question

Quizplus · Accepted Answer

The series is a geometric series with the first term $a = 5$ and common ratio $r = \frac{1}{5}$. The sum of a finite geometric series is given by $S_n = \frac{a(1 - r^n)}{1 - r}$, where $n$ is the number of terms. Here, $n = 5$, so $S_5 = \frac{5(1 - (\frac{1}{5})^5)}{1 - \frac{1}{5}} = \frac{5(1 - \frac{1}{3125})}{\frac{4}{5}} = \frac{5 \cdot \frac{3124}{3125}}{\frac{4}{5}} = \frac{3124}{625} = \frac{781}{125}$.

Find the Sum of the Geometric Series 5+1+15+125+11255 + 1 + \frac { 1 } { 5 } + \frac { 1 } { 25 } + \frac { 1 } { 125 }5+1+51​+251​+1251​

Find the Sum of the Geometric Series $5 + 1 + \frac { 1 } { 5 } + \frac { 1 } { 25 } + \frac { 1 } { 125 }$