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

Question

Answer 1

Let the given expression be denoted by E. Then

E = \frac{2024+2025}{2024+2025} + \frac{2024}{2025} + \frac{2025}{2026}

The first term simplifies to 1:

\frac{2024+2025}{2024+2025} = 1

The second and third terms are fractions close to 1. Let's approximate them:

\frac{2024}{2025} \approx 1 - \frac{1}{2025}

\frac{2025}{2026} \approx 1 - \frac{1}{2026}

Therefore,

E \approx 1 + (1 - \frac{1}{2025}) + (1 - \frac{1}{2026}) = 3 - \frac{1}{2025} - \frac{1}{2026}

Since

and

are small positive numbers,

is slightly less than 3.Let's calculate the second and third terms more precisely:

\frac{2024}{2025} \approx 0.9995037

\frac{2025}{2026} \approx 0.99950468

Adding these two terms:

0.9995037 + 0.99950468 \approx 1.99900838

Therefore,

E \approx 1 + 1.99900838 = 2.99900838

This confirms that E is slightly less than 3.To be more precise, we can calculate the exact value:

E = 1 + \frac{2024}{2025} + \frac{2025}{2026} \approx 1 + 0.9995037 + 0.99950468 \approx 2.99900838

Final Answer: The final answer is

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