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Home » Ryliebabyy Magic: You Won’t Believe What This Toy Did to My Baby’s First Smile! - Abbey Badges

Ryliebabyy Magic: You Won’t Believe What This Toy Did to My Baby’s First Smile! - Abbey Badges

📅 February 27, 2026 👤 scraface

Feb 27, 2026

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📌 Now compute the difference:

📌 E(t+1) - E(t) = a(t+1)^2 + b(t+1) - (at^2 + bt) = a(2t+1) + b = 2at + (a + b).

📌 Set equal to $ 2t + 1 $:

📌 2at + (a + b) = 2t + 1.

📌 2a = 2 \Rightarrow a = 1, \quad a + b = 1 \Rightarrow 1 + b = 1 \Rightarrow b = 0.

📌 Thus, $ E(t) = t^2 $.

📌 Then $ E(10) = 10^2 = 100 $.

📌 Alternatively, recognize the recurrence as the discrete analog of derivative; sum telescoping:

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