1. **Problem Statement:** Find the value of the series $$100 - 99 + 98 - 97 + 96 - 95 + \cdots + 2 - 1$$. 2. **Understanding the series:** The series alternates between subtracting and adding consecutive integers starting from 100 down to 1. 3. **Rewrite the series in pairs:** Group the terms in pairs: $$ (100 - 99) + (98 - 97) + (96 - 95) + \cdots + (2 - 1) $$ 4. **Evaluate each pair:** Each pair is of the form $$ (\text{even number}) - (\text{odd number just before it}) $$. For example, $$100 - 99 = 1$$, $$98 - 97 = 1$$, and so on. 5. **Count the number of pairs:** Since the series goes from 100 down to 1, there are 100 terms. Number of pairs = $$\frac{100}{2} = 50$$. 6. **Sum of all pairs:** Each pair sums to 1, so total sum is: $$50 \times 1 = 50$$. 7. **Final answer:** The value of the series is $$\boxed{50}$$. This corresponds to option (D).