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Home » Divide the entire equation by 3: - Redraw

Divide the entire equation by 3: - Redraw

📅 May 4, 2026 👤 scraface

May 04, 2026

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📌 $ T(4) = 2 \cdot 25 + 3 = 50 + 3 = 53 $

📌 $ T(5) = 2 \cdot 53 + 3 = 106 + 3 = 109 $

📌 Now compute the sum:

📌 S(5) = T(1) + T(2) + T(3) + T(4) + T(5) = 4 + 11 + 25 + 53 + 109 = 202

📌 Thus, the total energy over the first 5 segments is $ \boxed{202} $.

📌 Question: A computer graphics specialist models light intensity $ I(x) $ along a surface as $ I(x) = \frac{1}{x^2 + 4x + 5} $. If the cumulative visual effect over points $ x = 1 $ to $ x = n $ is modeled by $ C(n) = \sum_{x=1}^{n} I(x) $, find $ C(4) $.

📌 Solution: We evaluate $ I(x) = \frac{1}{x^2 + 4x + 5} $ at $ x = 1, 2, 3, 4 $:

📌 At $ x = 1 $: $ I(1) = \frac{1}{1^2 + 4 \cdot 1 + 5} = \frac{1}{10} $

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