Find the sum of the convergent series. $\sum _ { n = 0 } ^ { \infty } 9 \left( \frac { 8 } { 9 } \right) ^ { n }$
A) $81$
B) $63$
C) $72$
D)9
E)8

Question

Quizplus · Accepted Answer

This series is a geometric series with the first term $a = 9$ and common ratio $r = \frac{8}{9}$. The sum of a convergent geometric series is given by $S = \frac{a}{1 - r}$. Substituting $a = 9$ and $r = \frac{8}{9}$, we get $S = \frac{9}{1 - \frac{8}{9}} = \frac{9}{\frac{1}{9}} = 81$.

Find the Sum of the Convergent Series ∑n=0∞9(89)n\sum _ { n = 0 } ^ { \infty } 9 \left( \frac { 8 } { 9 } \right) ^ { n }∑n=0∞​9(98​)n

Find the Sum of the Convergent Series $\sum _ { n = 0 } ^ { \infty } 9 \left( \frac { 8 } { 9 } \right) ^ { n }$