1. **State the problem:** Calculate the sum $$\sum_{n=15}^{47} (2n - 5)$$. 2. **Formula and rules:** The summation of a linear expression can be split as $$\sum (2n - 5) = 2\sum n - 5\sum 1$$. 3. **Calculate the number of terms:** From $n=15$ to $n=47$, the number of terms is $$47 - 15 + 1 = 33$$. 4. **Sum of integers from 15 to 47:** Use the formula for the sum of an arithmetic series: $$\sum_{n=15}^{47} n = \frac{\text{number of terms} \times (\text{first term} + \text{last term})}{2} = \frac{33 \times (15 + 47)}{2} = \frac{33 \times 62}{2} = 33 \times 31 = 1023$$. 5. **Sum of constants:** $$\sum_{n=15}^{47} 1 = 33$$. 6. **Calculate the original sum:** $$\sum_{n=15}^{47} (2n - 5) = 2 \times 1023 - 5 \times 33 = 2046 - 165 = 1881$$. 7. **Final answer:** The value of the summation is **1881**.