1. **State the problem:** We need to find the value of the sum $$\sum_{n=2}^{43} 900(0.85)^{n-1}$$ and round it to the nearest integer. 2. **Identify the type of sum:** This is a geometric series with first term $$a = 900(0.85)^{1} = 900 \times 0.85$$ and common ratio $$r = 0.85$$. 3. **Formula for the sum of a geometric series:** For $$n$$ terms, the sum is $$S_n = a \frac{1-r^n}{1-r}$$. 4. **Calculate the number of terms:** From $$n=2$$ to $$n=43$$, there are $$43 - 2 + 1 = 42$$ terms. 5. **Calculate the first term:** $$a = 900 \times 0.85 = 765$$. 6. **Calculate the sum:** $$ S_{42} = 765 \times \frac{1 - (0.85)^{42}}{1 - 0.85} = 765 \times \frac{1 - (0.85)^{42}}{0.15} $$ 7. **Evaluate $$ (0.85)^{42} $$:** This is a very small number approximately $$0.0083$$. 8. **Substitute and simplify:** $$ S_{42} = 765 \times \frac{1 - 0.0083}{0.15} = 765 \times \frac{0.9917}{0.15} = 765 \times 6.6113 = 5055.65 $$ 9. **Round to nearest integer:** $$5056$$. **Final answer:** $$\boxed{5056}$$