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Home » As fraction: \( \frac168832 = \frac2114 \). - Portal da AcÃºstica

As fraction: \( \frac168832 = \frac2114 \). - Portal da AcÃºstica

📅 March 1, 2026 👤 scraface

Mar 01, 2026

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📌 A quantum computing cryptography expert is analyzing a security function \( M(v) = v - \frac{v^5}{5} \) for noise reduction. If \( m_n \) is defined by \( m_n = M\left(\frac{1}{n}\right) \), find the limit of \( m_n \) as \( n \to \infty \).

📌 We evaluate the limit of \( m_n = M\left(\frac{1}{n}\right) = \frac{1}{n} - \frac{\left(\frac{1}{n}\right)^5}{5} \) as \( n \to \infty \).

📌 Substitute into the function:

📌 m_n = \frac{1}{n} - \frac{1}{5n^5}

📌 Take the limit as \( n \to \infty \):

📌 \lim_{n \to \infty} \left( \frac{1}{n} - \frac{1}{5n^5} \right) = \lim_{n \to \infty} \frac{1}{n} - \lim_{n \to \infty} \frac{1}{5n^5}

📌 Both terms approach 0:

📌 \lim_{n \to \infty} \frac{1}{n} = 0 \quad \text{and} \quad \lim_{n \to \infty} \frac{1}{5n^5} = 0

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