The result of the given expression \(\Delta T(n) = \frac{2}{n(n + 1)} - 1\) when \(n = 114514\) is approximately \(-0.99999999985\).

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Here are 5 related questions to explore further:
1. What is the significance of the term \(\Delta T(n)\) in this context?
2. How does the value of \(n\) affect the behavior of the equation as \(n\) increases?
3. Can the equation be rewritten to highlight the asymptotic behavior as \(n \to \infty\)?
4. What are practical applications of equations in this form, involving large \(n\)?
5. How would the equation change if the \(+1\) in the denominator were modified?

**Tip:** When analyzing limits, check how expressions behave for large values of \(n\) to understand their long-term behavior.

Discover how to evaluate the expression ΔT(n) = 2/n(n + 1) − 1 for n = 114514. This solution covers key calculus concepts and limit theorems, offering insight into the behavior of sequences and series as n approaches infinity.

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