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lyrics life goes on long after the thrill - Crosslake

📅 March 1, 2026 👤 scraface

Mar 01, 2026

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📌 Width = 8 cm, Length = 16 cm

📌 #### Width: 8 cm, Length: 16 cmQuestion: Define $ F(n) = n - rac{n^2}{2} $ for every positive integer $ n $. If $ b_1 = 1 $ and $ b_{k+1} = F(b_k) $ for $ k \geq 1 $, compute $ b_5 $.

📌 Solution: We compute the sequence step by step using the definition of $ F(n) = n - rac{n^2}{2} $.

📌 Start with $ b_1 = 1 $.

📌 b_2 = F(b_1) = F(1) = 1 - rac{1^2}{2} = 1 - rac{1}{2} = rac{1}{2}

📌 b_3 = F(b_2) = F\left(rac{1}{2}

📌 ight) = rac{1}{2} - rac{1}{2} \left(rac{1}{2}

📌 ight)^2 = rac{1}{2} - rac{1}{2} \cdot rac{1}{4} = rac{1}{2} - rac{1}{8} = rac{3}{8}

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