Find the sum. \[ \frac{1}{8}+\frac{5}{8}+\frac{5^{2}}{8}+\frac{5^{3}}{8}+\cdots+\frac{5^{n-1}}{8} \] Complete the sum of the sequence. \[ s_{n}=\square\left(\square^{n}-1\right) \] (Type an integer or a simplified fraction.)

Step 1 ：We are given a geometric series with the first term a = 1/8 and the common ratio r = 5.

Step 2 ：The sum of the first n terms of a geometric series can be calculated using the formula: \(s_{n} = a \cdot \frac{1 - r^n}{1 - r}\)

Step 3 ：Substitute a = 1/8 and r = 5 into the formula to find the sum of the series.

Step 4 ：\(s_{n} = 0.125 \cdot \frac{1 - 5^n}{1 - 5}\)

Step 5 ：Simplify the expression to get the final answer.

Step 6 ：\(s_{n} = \frac{1}{32} \cdot (5^n - 1)\)

Step 7 ：\(\boxed{s_{n} = \frac{1}{32} \cdot (5^n - 1)}\)