Find the sum of the series, if possible.
-$$\sum _ { i = 1 } ^ { \infty } \left( \frac { 3 } { 5 } \right) ^ { i }$$
A) $- \frac { 3 } { 2 }$
B) $\frac { 3 } { 2 }$
C) Not possible, infinite
D) $\frac { 5 } { 2 }$

Question

Quizplus · Accepted Answer

This series is a geometric series with the first term $a = \left(\frac{3}{5}\right)^1 = \frac{3}{5}$ and common ratio $r = \frac{3}{5}$. The sum of an infinite geometric series is given by $S = \frac{a}{1 - r}$, provided $|r| < 1$. Substituting $a = \frac{3}{5}$ and $r = \frac{3}{5}$, we get $S = \frac{\frac{3}{5}}{1 - \frac{3}{5}} = \frac{\frac{3}{5}}{\frac{2}{5}} = \frac{3}{2}$.

Find the Sum of the Series, If Possible ∑i=1∞(35)i\sum _ { i = 1 } ^ { \infty } \left( \frac { 3 } { 5 } \right) ^ { i }i=1∑∞​(53​)i

Find the Sum of the Series, If Possible $\sum _ { i = 1 } ^ { \infty } \left( \frac { 3 } { 5 } \right) ^ { i }$