1. **State the problem:** We need to evaluate the infinite series $$\sum_{n=1}^\infty \frac{2^{5n}}{3^{2n}}$$. 2. **Rewrite the series:** Note that $$2^{5n} = (2^5)^n = 32^n$$ and $$3^{2n} = (3^2)^n = 9^n$$. So the series becomes $$\sum_{n=1}^\infty \left(\frac{32}{9}\right)^n$$. 3. **Check convergence:** Since $$\frac{32}{9} > 1$$, the terms do not approach zero and the series diverges. 4. **Conclusion:** The infinite series $$\sum_{n=1}^\infty \frac{2^{5n}}{3^{2n}}$$ diverges and does not have a finite sum. --- **Regarding the drone coverage mapping problem:** The user requests a mathematical answer for drone coverage y related to multiple drone scanning paths forming an envelope. Since no explicit function or formula is given, we can model the envelope of coverage as the union of paths. A common approach is to represent each drone path as a parametric function and then find the envelope by taking the maximum coverage at each point. For simplicity, assume the drone scanning paths can be modeled as functions $$y_i = f_i(x)$$ for $$i=1,2,\ldots$$. The envelope $$y$$ is then: $$ y = \max_i f_i(x) $$ This maximizes coverage and helps minimize blind spots. Without explicit functions, the best we can do is state this general approach. --- **Summary:** - The infinite series diverges. - The drone coverage envelope can be modeled as $$y = \max_i f_i(x)$$ to minimize blind spots.