1. **State the problem:** We need to find the value of $$n = 1^2 + 1^4 + 1^6 + 1^8 + \ldots + 1^{50}$$. 2. **Understand the terms:** Each term is $$1$$ raised to an even power from 2 to 50. 3. **Recall the property:** For any integer $$k$$, $$1^k = 1$$. 4. **Count the number of terms:** The powers are even numbers starting at 2 and ending at 50. 5. **Number of even integers from 2 to 50:** The sequence is 2, 4, 6, ..., 50. 6. The number of terms is $$\frac{50}{2} = 25$$. 7. **Sum all terms:** Since each term is 1, the sum is $$25 \times 1 = 25$$. **Final answer:** $$n = 25$$, which corresponds to option C.