(2024+2025)/(2025+2026)+(2024)/(2025)+(2025)/(2026)

Let the given expression be denoted by E. Then<br />$$E = \frac{2024+2025}{2024+2025} + \frac{2024}{2025} + \frac{2025}{2026}$$<br />The first term simplifies to 1:<br />$$\frac{2024+2025}{2024+2025} = 1$$<br />The second and third terms are fractions close to 1. Let's approximate them:<br />$$\frac{2024}{2025} \approx 1 - \frac{1}{2025}$$<br />$$\frac{2025}{2026} \approx 1 - \frac{1}{2026}$$<br />Therefore,<br />$$E \approx 1 + (1 - \frac{1}{2025}) + (1 - \frac{1}{2026}) = 3 - \frac{1}{2025} - \frac{1}{2026}$$<br />Since $\frac{1}{2025}$ and $\frac{1}{2026}$ are small positive numbers, $E$ is slightly less than 3.<br /><br />Let's calculate the second and third terms more precisely:<br />$$\frac{2024}{2025} \approx 0.9995037$$<br />$$\frac{2025}{2026} \approx 0.99950468$$<br />Adding these two terms:<br />$$0.9995037 + 0.99950468 \approx 1.99900838$$<br />Therefore,<br />$$E \approx 1 + 1.99900838 = 2.99900838$$<br />This confirms that E is slightly less than 3.<br /><br />To be more precise, we can calculate the exact value:<br />$$E = 1 + \frac{2024}{2025} + \frac{2025}{2026} \approx 1 + 0.9995037 + 0.99950468 \approx 2.99900838$$<br /><br />Final Answer: The final answer is $\boxed{3}$