Final answer:
Utilizing the properties of the given functional equation, we deduce that f(n) = 2^n and each term in the series reduces to 2. The sum of the series is the number of terms multiplied by 2, resulting in a final answer of 4040.
Step-by-step explanation:
We are given a functional equation f(x+y) = f(x) \u2022 f(y) and a specific function value f(1) = 2. This type of function is known as an exponential function. To find each term in the series f(2)/f(1) + f(3)/f(2) + ... + f(2021)/f(2020), we can apply the properties of the given function.
For example, f(2) can be found by considering it as f(1+1), which by property of the function is f(1) \u2022 f(1), and hence is 2 \u2022 2 = 4. So, f(2)/f(1) = 4/2 = 2.
Using the same property recursively to find each subsequent term, we see that f(n) = 2^n for a positive integer n. This pattern holds for all terms in the series, making each fraction equal to 2. Consequently, the value of the entire series is 2 multiplied by the number of terms, which is 2021 - 1 = 2020 terms.
Therefore, the final answer is 2 \u2022 2020 = 4040.