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bipolar 1 vs 2 disorder - Richter Guitar

📅 May 4, 2026 👤 scraface

May 04, 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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