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Home » Clypeasteroida Secrets: The Jaw-Dropping Fossil You Need to See Now! - Feedz API

Clypeasteroida Secrets: The Jaw-Dropping Fossil You Need to See Now! - Feedz API

📅 May 18, 2026 👤 scraface

May 18, 2026

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📌 Question:** A sequence of neural response intensities in a human-machine interface is defined by \(a_n = \frac{n^2 + 1}{n + 1}\). Simplify \(a_n\) and find the value when \(n = 4\).

📌 We simplify the expression:

📌 a_n = \frac{n^2 + 1}{n + 1}

📌 We attempt polynomial division or rewrite the numerator:

📌 Note that \(n^2 + 1\) does not factor nicely over integers, so perform direct substitution for \(n = 4\):

📌 a_4 = \frac{4^2 + 1}{4 + 1} = \frac{16 + 1}{5} = \frac{17}{5}

📌 Thus, the simplified form evaluated at \(n = 4\) is:

📌 \boxed{\frac{17}{5}}

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