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Home » Speech Blubs Secret: How to Shatter Quirks in Just 7 Days! - Sterling Industries

Speech Blubs Secret: How to Shatter Quirks in Just 7 Days! - Sterling Industries

📅 April 18, 2026 👤 scraface

Apr 18, 2026

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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...
L = f(L) = L - \frac{L^4}{4} \Rightarrow \frac{L^4}{4} = 0 \Rightarrow...
Thus, the sequence converges to $ \boxed{0} $.

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