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Home » + 26 = 93 \text million miles - Silent Sales Machine

+ 26 = 93 \text million miles - Silent Sales Machine

📅 March 10, 2026 👤 scraface

Mar 10, 2026

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📌 Substituting into the expression:

📌 x^4 + 4x^2 + 3 = (u^2 - 4u + 4) + 4(u - 2) + 3 = u^2 - 4u + 4 + 4u - 8 + 3 = u^2 - 1.

📌 f(u) = u^2 - 1.

📌 Now substitute $ u = x^2 - 2 $ into $ f $:

📌 f(x^2 - 2) = (x^2 - 2)^2 - 1 = x^4 - 4x^2 + 4 - 1 = x^4 - 4x^2 + 3.

📌 \boxed{x^4 - 4x^2 + 3}

📌 Question: Compute $ \sum_{n=1}^{50} \frac{1}{n(n+2)} $.

📌 Solution: We begin by simplifying the general term using partial fractions:

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