Evaluate the sum.
-$$\sum _ { i = 1 } ^ { 5 } \left( \frac { 1 } { 5 } \right) ^ { i }$$

Question

Quizplus · Accepted Answer

This sum is a geometric series with the first term $a = \left(\frac{1}{5}\right)^1 = \frac{1}{5}$, common ratio $r = \frac{1}{5}$, and $n = 5$ terms. The sum of a geometric series is given by $S_n = \frac{a(1 - r^n)}{1 - r}$. Plugging in the values, we get $S_5 = \frac{\frac{1}{5}(1 - (\frac{1}{5})^5)}{1 - \frac{1}{5}} = \frac{\frac{1}{5}(1 - \frac{1}{3125})}{\frac{4}{5}} = \frac{1 - \frac{1}{3125}}{4} = \frac{3124}{3125 \cdot 4} = \frac{781}{3125}$.

Evaluate the Sum ∑i=15(15)i\sum _ { i = 1 } ^ { 5 } \left( \frac { 1 } { 5 } \right) ^ { i }i=1∑5​(51​)i

Evaluate the Sum $\sum _ { i = 1 } ^ { 5 } \left( \frac { 1 } { 5 } \right) ^ { i }$