Unformatted text preview: 1. lim n →∞ n b a n = 0, for a > 1 and any b . 2. lim n →∞ a n n ! = 0, for any a . 3. lim n →∞ n ! n n = 0. 4. lim n →∞ n + 1 n = 1; more generally 5. lim n →∞ ( n + 1) b n b = 1 for any power b ; and more generally still 6. lim n →∞ p ( n + 1) p ( n ) = 1 for any polynomial p ( n ). 7. lim n →∞ a n +1 a n = a n +1 a n = a (geometric). 8. ( n + 1)! n ! = n + 1, so 9. lim n →∞ ( n + 1)! n ! = ∞ (factorial). 10. lim n →∞ n 1 /n = 1 and more generally 11. lim n →∞  p ( n )  1 /n = 1 for any polynomial p ( n ). 12. lim n →∞  a n  1 /n =  a  (geometric). 13. lim n →∞ ( n !) 1 /n = ∞ (factorial)....
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 Spring '08
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 Calculus, lim, Prime number

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