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what did rutherford discover - Imagemakers

📅 April 30, 2026 👤 scraface

Apr 30, 2026

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📌 \Rightarrow 0 = -rac{L^3}{6}

📌 \Rightarrow L^3 = 0 \Rightarrow L = 0

📌 We verify convergence. Since \( f(t) = t\left(1 - rac{t^2}{6}

📌 ight) \), for \( t > 0 \), \( f(t) < t \) when \( 1 - rac{t^2}{6} < 1 \), which is always true, but more importantly, for \( t \in (0, \sqrt{6}) \), \( c_{n+1} = f(c_n) < c_n \). With \( c_1 = 0.5 \), compute:

📌 c_2 = f(0.5) = 0.5 - rac{(0.5)^3}{6} = 0.5 - rac{0.125}{6} = 0.5 - 0.020833 pprox 0.479167

📌 Decreasing and bounded below by 0, so convergent. The only fixed point is \( L = 0 \), hence:

📌 \lim_{n o \infty} c_n = 0

📌 Question: A science communicator creates a puzzle involving the equation

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