Unformatted text preview: x → ∞ . So by the Squeeze Theorem, lim x →∞ f ( x ) = ∞ , and thus lim n →∞ a n = ∞ as well. 2. (3 pts) b n = n ! 11 n There are many ways to show that this approaches in±nity. As one possibility, observe that whatever b 21 is, it is positive, and that for n ≥ 22 we have: b n b n1 = n ! 11 n · 11 n1 ( n1)! = n 11 ≥ 2 So b 22 ≥ 2 b 21 , and b 23 ≥ 2 b 22 ≥ 2 2 b 21 , and b 24 ≥ 2 b 23 ≤ 2 3 b 21 , and so on. In general, for any positive n we have b 21+ n ≥ 2 n b 21 > 0, and since the middle term grows without bound, lim n →∞ b n = ∞ ....
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 Spring '09
 CHRIST
 Calculus

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