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Home » 5.Hear the Hidden ‘Thwomp’ Sound That’s Secretly Changing Soundtrack Hypes! - Network4

5.Hear the Hidden ‘Thwomp’ Sound That’s Secretly Changing Soundtrack Hypes! - Network4

📅 May 19, 2026 👤 scraface

May 19, 2026

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Question: Define $ f(u) = u - \frac{u^4}{4} $. If $ n $ is a positive...
b_1 = 1, \quad b_{n+1} = f(b_n).
Determine the limit $ \lim_{n \to \infty} b_n $.
Solution: We are given the recurrence
b_1 = 1, \quad b_{n+1} = f(b_n), \quad \text{where } f(u) = u - \frac{...
We aim to find $ \lim_{n \to \infty} b_n $.
First, observe that $ f(u) < u $ for all $ u > 0 $, since $ \frac{u^4}...
Taking limits on both sides of the recurrence:
\lim_{n \to \infty} b_{n+1} = \lim_{n \to \infty} f(b_n) = f(L).
But since $ \lim_{n \to \infty} b_{n+1} = \lim_{n \to \infty} b_n = L...

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