Find the sum.
-$$\sum _ { \mathrm { k } = 1 } ^ { 3 } \left( \frac { 2 } { 3 } \right) ^ { \mathrm { k } + 1 }$$
A) $\frac { 38 } { 27 }$

B) $\frac { 76 } { 81 }$

C) $\frac { 260 } { 81 }$

D) $\frac { 80 } { 81 }$

Question

Find the sum.
-$$\sum _ { \mathrm { k } = 1 } ^ { 3 } \left( \frac { 2 } { 3 } \right) ^ { \mathrm { k } + 1 }$$
A) $\frac { 38 } { 27 }$

B) $\frac { 76 } { 81 }$

C) $\frac { 260 } { 81 }$

D) $\frac { 80 } { 81 }$

Quizplus · Accepted Answer

The sum is a geometric series with the first term $\left(\frac{2}{3}\right)^2$ and common ratio $\frac{2}{3}$. The sum of the series is $\frac{\left(\frac{2}{3}\right)^2(1-\left(\frac{2}{3}\right)^3)}{1-\frac{2}{3}}$, which simplifies to $\frac{76}{81}$.

Find the Sum ∑k=13(23)k+1\sum _ { \mathrm { k } = 1 } ^ { 3 } \left( \frac { 2 } { 3 } \right) ^ { \mathrm { k } + 1 }k=1∑3​(32​)k+1

Find the Sum $\sum _ { \mathrm { k } = 1 } ^ { 3 } \left( \frac { 2 } { 3 } \right) ^ { \mathrm { k } + 1 }$