Evaluate the series, if it converges.
-$$\sum _ { k = 1 } ^ { \infty } \left( \frac { 3 } { 8 } \right) ^ { k }$$
A) Does not converge.
B) $\frac { 3 } { 5 }$
C) $ - \frac { 3 } { 5 }$
D) $\frac { 8 } { 5 }$

Question

Quizplus · Accepted Answer

This series is a geometric series with the first term $a = \left( \frac{3}{8} \right)^1 = \frac{3}{8}$ and common ratio $r = \frac{3}{8}$. The sum of an infinite geometric series is given by $S = \frac{a}{1 - r}$, provided $|r| < 1$. Substituting the given values, we get $S = \frac{\frac{3}{8}}{1 - \frac{3}{8}} = \frac{\frac{3}{8}}{\frac{5}{8}} = \frac{3}{5}$.

Evaluate the Series, If It Converges ∑k=1∞(38)k\sum _ { k = 1 } ^ { \infty } \left( \frac { 3 } { 8 } \right) ^ { k }k=1∑∞​(83​)k

Evaluate the Series, If It Converges $\sum _ { k = 1 } ^ { \infty } \left( \frac { 3 } { 8 } \right) ^ { k }$