To evaluate the related series of the given sequence $2, 1, \frac{1}{2}, \frac{1}{4}, \frac{1}{8}$, we need to find the sum of all these terms.

Let's go through the calculation step-by-step:

1. Write the sequence in terms of fractions with a common denominator, or evaluate the sum directly as they appear.

2. The sequence terms are: $2 = \frac{16}{8}, \quad 1 = \frac{8}{8}, \quad \frac{1}{2} = \frac{4}{8}, \quad \frac{1}{4} = \frac{2}{8}, \quad \frac{1}{8}$

3. Adding these values: $\frac{16}{8} + \frac{8}{8} + \frac{4}{8} + \frac{2}{8} + \frac{1}{8} = \frac{16 + 8 + 4 + 2 + 1}{8} = \frac{31}{8}$

Thus, the correct answer is: $\frac{31}{8}$

The answer that corresponds to this value in the options is $\boxed{\frac{31}{8}}$.

Would you like a deeper explanation of any part of the process? Here are some related questions you might find helpful:

1. How do you find a common denominator when adding fractions?
2. What methods can be used to verify the sum of a series?
3. How can you convert mixed numbers to improper fractions for series calculations?
4. What are some strategies to simplify complex fractions quickly?
5. How does this series relate to a geometric sequence?

Tip: When adding fractions, converting all terms to a common denominator simplifies the process and helps ensure accuracy.