Find the sum of the convergent series. $$\sum _ { n = 0 } ^ { \infty } 9 \left( \frac { 4 } { 5 } \right) ^ { n }$$
A) 4
B) 36
C) 9
D) 27
E) 45

Question

Quizplus · Accepted Answer

This series is a geometric series with the first term $a = 9$ and common ratio $r = \frac{4}{5}$. The sum of an infinite geometric series is given by $S = \frac{a}{1 - r}$, where $|r| < 1$. Substituting $a = 9$ and $r = \frac{4}{5}$, we get $S = \frac{9}{1 - \frac{4}{5}} = \frac{9}{\frac{1}{5}} = 9 \times 5 = 45$.

Find the Sum of the Convergent Series ∑n=0∞9(45)n\sum _ { n = 0 } ^ { \infty } 9 \left( \frac { 4 } { 5 } \right) ^ { n }n=0∑∞​9(54​)n

Find the Sum of the Convergent Series $\sum _ { n = 0 } ^ { \infty } 9 \left( \frac { 4 } { 5 } \right) ^ { n }$