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Home » Each gives 4 non-prime even-even combinations → 24 - Blask

Each gives 4 non-prime even-even combinations → 24 - Blask

📅 March 10, 2026 👤 scraface

Mar 10, 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} $.

📝 Recent Posts

French speakers: 0.52 × 1500 = <<0.52*1500=780>>780.
Both: 0.35 × 1500 = <<0.35*1500=525>>525.
Only English: 1170 – 525 = <<1170-525=645>>645.
Only French: 780 – 525 = <<780-525=255>>255.
Total bilingual or monolingual speakers: 645 + 255 + 525 = <<645+255+5...
Speak neither: 1500 – 1425 = <<1500-1425=75>>75.
An environmental historian analyzes 100 square kilometers of land in W...
In 1850, forest: 0.50 × 100 = <<0.50*100=50>>50 km².
Converted to farmland by 1900: 0.40 × 50 = <<0.40*50=20>>20 km².
Remaining forest in 1900: 50 – 20 = <<50-20=30>>30 km².

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