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Home » \left\lceil \frac10036 \right\rceil = \left\lceil 2.777\ldots \right\rceil = 3 - DNSFLEX

\left\lceil \frac10036 \right\rceil = \left\lceil 2.777\ldots \right\rceil = 3 - DNSFLEX

📅 March 11, 2026 👤 scraface

Mar 11, 2026

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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} $.
To confirm convergence, note that $ f(u) $ is continuous and decreasin...
Question: Let $ p(x) $ be a polynomial such that

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