Evaluate the series, if it converges.
-$$\sum _ { \mathrm { k } = 1 } ^ { \infty } \left( \frac { 3 } { 10 } \right) ^ { \mathrm { k } }$$
A) Does not converge.
B) $\frac { 10 } { 7 }$
C) $\frac { 3 } { 7 }$
D) $- \frac { 3 } { 7 }$

Question

Quizplus · Accepted Answer

The series is a geometric series with first term $a = \frac{3}{10}$ and common ratio $r = \frac{3}{10}$. Since $|r| < 1$, the series converges to $\frac{a}{1-r} = \frac{\frac{3}{10}}{1-\frac{3}{10}} = \frac{3}{7}$.

Evaluate the Series, If It Converges ∑k=1∞(310)k\sum _ { \mathrm { k } = 1 } ^ { \infty } \left( \frac { 3 } { 10 } \right) ^ { \mathrm { k } }k=1∑∞​(103​)k

Evaluate the Series, If It Converges $\sum _ { \mathrm { k } = 1 } ^ { \infty } \left( \frac { 3 } { 10 } \right) ^ { \mathrm { k } }$