Find the sum. $\sum_{n=0}^{\infty}\left(-\frac{3}{8}\right)^{n}$
A) $\frac{8}{11}$
B) $\frac{3}{14}$
C) $\frac{5}{8}$
D) $\frac{8}{5}$
E) $\frac{3}{5}$

Question

Quizplus · Accepted Answer

This is a geometric series with the first term $a = 1$ (since $(-3/8)^0 = 1$) and common ratio $r = -3/8$. The sum of an infinite geometric series is given by $S = \frac{a}{1 - r}$, provided $|r| < 1$. Substituting $a = 1$ and $r = -3/8$, we get $S = \frac{1}{1 - (-3/8)} = \frac{1}{1 + 3/8} = \frac{1}{11/8} = \frac{8}{11}$.

Find the Sum ∑n=0∞(−38)n\sum_{n=0}^{\infty}\left(-\frac{3}{8}\right)^{n}∑n=0∞​(−83​)n A) 811\frac{8}{11}118​ B) 314\frac{3}{14}143​ C) 58\frac{5}{8}85​ D) 85\frac{8}{5}58​ E) 35\frac{3}{5}53​

Find the Sum $\sum_{n=0}^{\infty}\left(-\frac{3}{8}\right)^{n}$ A) $\frac{8}{11}$ B) $\frac{3}{14}$ C) $\frac{5}{8}$ D) $\frac{8}{5}$ E) $\frac{3}{5}$