Find the sum.
-$$\sum _ { k = 2 } ^ { 5 } \left( \frac { 1 } { 3 } \right) ^ { k }$$

Question

Quizplus · Accepted Answer

The sum of the series is calculated by adding the terms from $k = 2$ to $k = 5$ of the sequence $\left( \frac { 1 } { 3 } \right) ^ { k }$. This results in $\left( \frac { 1 } { 3 } \right) ^ { 2 } + \left( \frac { 1 } { 3 } \right) ^ { 3 } + \left( \frac { 1 } { 3 } \right) ^ { 4 } + \left( \frac { 1 } { 3 } \right) ^ { 5 }$, which simplifies to $\frac { 1 } { 9 } + \frac { 1 } { 27 } + \frac { 1 } { 81 } + \frac { 1 } { 243 }$. Adding these fractions together gives $\frac { 40 } { 243 }$.

Find the Sum ∑k=25(13)k\sum _ { k = 2 } ^ { 5 } \left( \frac { 1 } { 3 } \right) ^ { k }k=2∑5​(31​)k

Find the Sum $\sum _ { k = 2 } ^ { 5 } \left( \frac { 1 } { 3 } \right) ^ { k }$