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Home » \( h(0) = 3 \) implies \( c = 3 \). - AMAZONAWS

\( h(0) = 3 \) implies \( c = 3 \). - AMAZONAWS

📅 March 5, 2026 👤 scraface

Mar 05, 2026

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📌 Define \( L(u) = u - rac{u^3}{3} \) for every real number \( u \). If \( n \) is a positive integer, define \( a_n \) by \( a_1 = rac{1}{2} \), \( a_{n+1} = L(a_n) \). Find \( \lim_{n o \infty} a_n \).

📌 We are given a recursive sequence:

📌 \( a_1 = rac{1}{2} \)

📌 \( a_{n+1} = L(a_n) = a_n - rac{a_n^3}{3} \)

📌 We seek \( \lim_{n o \infty} a_n \), assuming the limit exists and equals \( L \).

📌 If the limit exists, then:

📌 L = L - rac{L^3}{3} \Rightarrow rac{L^3}{3} = 0 \Right

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