Show that lim⁡n→∞(21⋅32⋅43⋯nn−1)1/n=1\lim_{n \to \infty} \left(... | Filo
Show that lim⁡n→∞(21⋅32⋅43⋯nn−1)1/n=1\li…
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🎓 Limite di (2n)! / nⁿ per n → ∞ Nel video lo risolvo con il criterio del rapporto 📈 Ma guarda anche questo metodo alternativo👇 Osserviamo che possiamo riscrivere (2n)! così: (2n)! / nⁿ = = (2n / n) × ((2n − 1) / n) × ((2n − 2) / n) × ... × ((n 1) / n) × n! Ogni termine del tipo (2n − k) / n, con k ≥ 0, è maggiore di 1. Quindi, nel complesso: (2n)! / nⁿ > n! E poiché n! → ∞, concludiamo che: lim (2n)! / nⁿ = ∞ 🧠 Volendo, si può anche usare la formula di Stirling per un approccio più raffinat
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🎓 Limite di (2n)! / nⁿ per n → ∞ Nel video lo risolvo con il criterio del r…
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