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**Unformatted text preview: **6. If a n ≤ x n ≤ b n and lim n →∞ a n = lim n →∞ b n = L , show that lim n →∞ x n = L . (This is sometimes called the sandwich theorem). 7. If b ≤ x n ≤ c for all but a ﬁnite number of n , show that b ≤ lim inf n →∞ x n , and lim sup n →∞ x n ≤ c. 8. Find lim inf n →∞ and lim sup n →∞ when: 1 2 (a) a n = (-1) n ± 2 + 3 n ² . (b) a n = n + (-1) n (2 n + 1) n ....

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